{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":10,"width":60,"type_input":"","input_hint":["frac"],"ques":"Cho A = $5 . 4^{15} . 9^9 - 4 . 3^{20} . 8^9$ <br\/> B = $5 . 2^9 . 6^{19} - 7 . 2^{29} . 27^6$ <br\/> V\u1eady A : B = _input_","hint":"Bi\u1ebfn \u0111\u1ed5i sau \u0111\u00f3 nh\u00f3m c\u00e1c nh\u00e2n t\u1eed chung \u1edf t\u1eed v\u00e0 m\u1eabu, sau \u0111\u00f3 tri\u1ec7t ti\u00eau c\u00e1c th\u1eeba s\u1ed1 gi\u1ed1ng nhau","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Chuy\u1ec3n c\u00e1c th\u1eeba s\u1ed1 c\u00f3 th\u1ec3 v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 2 ho\u1eb7c c\u01a1 s\u1ed1 3 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Th\u1ef1c hi\u1ec7n nh\u00e2n c\u00e1c l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 <br\/> <b> B\u01b0\u1edbc 3 : <\/b> Nh\u00f3m c\u00e1c th\u1eeba s\u1ed1 chung ra ngo\u00e0i r\u1ed3i r\u00fat g\u1ecdn <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/>$\\begin{align*} & \\dfrac{5 . 4^{15} . 9^9 - 4 . 3^{20} . 8^9}{5 . 2^9 . 6^{19} - 7 . 2^{29} . 27^6} \\\\\\\\ =& \\dfrac{5 . (2^2)^{15} . (3^2)^9 - 2^2 . 3^{20} . (2^3)^{9}}{5 . 2^9 . (2 . 3)^{19} - 7 . 2^{29}.3^{18}} \\\\\\\\ =& \\dfrac{5 . 2^{30} . 3^{18} - 2^2 . 3^{20} . 2^{27}}{5 . 2^9 . 2^{19} . 3^{19} - 7 . 2^{29} . 3^{18}} \\\\\\\\ =&\\dfrac{5 . 2^{30} . 3^{18} - 3^{20}.2^{29}}{5 . 2^{9 + 19} . 3^{19} - 7 . 2^{29} . 3^{18}} \\\\\\\\ =& \\dfrac{2^{29} . 3^{18} . (5 . 2 - 3^2)}{2^{28} . 3^{18} .(5 . 3 - 7 . 2)} \\\\\\\\=& \\dfrac{2 . (10 - 9)}{15 - 14} \\\\\\\\=& \\dfrac{2}{1} \\\\\\\\ =& 2\\end{align*}$<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 2 <\/span> "}]}],"id_ques":841},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" T\u00ednh. <br\/> $16 . 64 . 8^2 : (4^3 . 2^5 . 16)$ = _input_","hint":"Bi\u1ebfn \u0111\u1ed5i t\u1ea5t c\u1ea3 v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 2","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a $16, 64, 8^2, 4^3$ v\u1ec1 d\u1ea1ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 2 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Th\u1ef1c hi\u1ec7n nh\u00e2n, chia c\u00e1c l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/>$\\begin{align*} &16 . 64 . 8^2 : (4^3 . 2^5 . 16) \\\\\\\\ =& 2^4 . 2^6 . (2^3)^2 : ((2^2)^3 . 2^5 . 2^4) \\\\\\\\ =& 2^4 . 2^6 . 2^{3 . 2} : (2^{2 . 3} . 2^5 . 2^4) \\\\\\\\ =& 2^{4 + 6 + 6} : 2^{6 + 5 + 4} \\\\\\\\ =& 2^{16} : 2^{15} \\\\\\\\ =& 2^{16 - 15} \\\\\\\\ =& 2 \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 2 <\/span> "}]}],"id_ques":842},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["42"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai17/lv3/img\/2.jpg' \/><\/center> <br\/> T\u00ecm x bi\u1ebft $(2x + 2^4) . 5^3 = 4 . 5^5$ <br\/> V\u1eady x = _input_","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Coi $(2x + 2^4)$ l\u00e0 th\u1eeba s\u1ed1 ch\u01b0a bi\u1ebft <br\/> Mu\u1ed1n t\u00ecm th\u1eeba s\u1ed1 ch\u01b0a bi\u1ebft ta l\u1ea5y t\u00edch chia cho th\u1eeba s\u1ed1 \u0111\u00e3 bi\u1ebft <br\/> <b> B\u01b0\u1edbc 2: <\/b> Coi 2x l\u00e0 s\u1ed1 h\u1ea1ng ch\u01b0a bi\u1ebft <br\/> Mu\u1ed1n t\u00ecm s\u1ed1 h\u1ea1ng ch\u01b0a bi\u1ebft ta l\u1ea5y t\u1ed5ng tr\u1eeb \u0111i s\u1ed1 h\u1ea1ng \u0111\u00e3 bi\u1ebft <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/> $\\begin{align*} (2x + 2^4) . 5^3 =& 4 . 5^5 \\\\ 2x + 2^4 =& 4 . 5^5 : 5^3 \\\\ 2x + 16 =& 4 . 5^{5 - 3} \\\\ 2x + 16 =& 4 . 5^2 \\\\ 2x =& 4 . 25 - 16 \\\\ 2x =& 100 - 16 \\\\ 2x =& 84 \\\\ x =& 84 : 2 \\\\ x =& 42 \\end{align*} $ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 42 <\/span> "}]}],"id_ques":843},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["252"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai17/lv3/img\/12.jpg' \/><\/center> <br\/> T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean a bi\u1ebft: a $\\vdots$ 12; a $\\vdots$ 21; a $\\vdots$ 28 v\u00e0 170 < a < 300 <br\/> V\u1eady a = _input_ ","hint":"a $\\in$ BC(12; 21; 28) ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> V\u00ec a $\\vdots$ 12; a $\\vdots$ 21 v\u00e0 a $\\vdots$ 28 $\\Rightarrow$ a $\\in$ BC(12; 21; 28) <br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ecm BCNN(12; 21; 28) = ? <br\/> <b> B\u01b0\u1edbc 2: <\/b>T\u00ecm BC(12; 21; 28) b\u1eb1ng c\u00e1ch l\u1ea5y BCNN nh\u00e2n l\u1ea7n l\u01b0\u1ee3t v\u1edbi 0, 1, 2,... <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ecm a $\\in$ BC(12; 21; 28) v\u00e0 th\u1ecfa m\u00e3n 170 < a < 300 <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>V\u00ec a $\\vdots$ 12; a $\\vdots$ 21 v\u00e0 a $\\vdots$ 28 $\\Rightarrow$ a $\\in$ BC(12; 21; 28) <br\/> Ta c\u00f3: $12 = 2^2 . 3$; $21 = 3 . 7$ ; $28 = 2^2 . 7$ <br\/> $\\Rightarrow$ BCNN(12; 21; 28) = $2^2 . 3 . 7 = 84$ <br\/> $\\Rightarrow$ BC(12; 21; 28) = {0; 84; 168; 252; 336;...} <br\/> V\u00ec a $\\in$ BC(12; 21; 28) v\u00e0 170 < a < 300 $\\Rightarrow$ a = 252 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 252 <\/span> "}]}],"id_ques":844},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai17/lv3/img\/5.jpg' \/><\/center> <br\/> $107^{50}$ _input_ $73^{75}$ ","hint":"Ta \u0111i so s\u00e1nh $108^{50}$ v\u00e0 $72^{75}$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> V\u00ec 107 v\u00e0 73 l\u00e0 nh\u1eefng s\u1ed1 nguy\u00ean t\u1ed1 n\u00ean ta kh\u00f4ng bi\u1ebfn \u0111\u1ed5i \u0111\u01b0\u1ee3c <br\/> M\u00e0 $107^{50} < 108^{50}$ v\u00e0 $73^{75} > 72^{75}$ <br\/> N\u00ean ta \u0111i so s\u00e1nh $108^{50}$ v\u1edbi $72^{75}$ <br\/> Bi\u1ebfn \u0111\u1ed5i 108 v\u00e0 72 v\u1ec1 d\u1ea1ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 2 v\u00e0 3 \u0111\u1ec3 so s\u00e1nh <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec 107 v\u00e0 73 l\u00e0 nh\u1eefng s\u1ed1 nguy\u00ean t\u1ed1, kh\u00f4ng bi\u1ebfn \u0111\u1ed5i \u0111\u01b0\u1ee3c n\u00ean ta s\u1eed d\u1ee5ng c\u00e1c s\u1ed1 trung gian <br\/> Ta c\u00f3: $107^{50} < 108^{50}$ v\u00e0 $73^{75} > 72^{75}$ <br\/> $108^{50} = (4 . 27)^{50} = (2^2 . 3^3)^{50} = 2^{2 . 50} . 3^{3 . 50} = 2^{100} . 3^{150}$ <br\/> $72^{75} = (8 . 9)^{75} = (2^3 . 3^2)^{75} = 2^{3 . 75} . 3^{2 . 75} = 2^{225} . 3^{150}$ <br\/> V\u00ec $2^{100} . 3^{150}$ < $2^{225} . 3^{150}$ <br\/> N\u00ean $108^{50} < 72^{75}$ $\\Rightarrow$ $107^{50} < 73^{75}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: < <\/span> "}]}],"id_ques":845},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["48"],["84"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean , b bi\u1ebft 12 < a < b; BCNN(a, b) = 336 v\u00e0 \u01afCLN(a, b) = 12 <br\/> V\u1eady a = _input_; b = _input_ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> V\u00ec \u01afCLN(a, b) = 12 $\\Rightarrow$ $\u01afCLN \\left( \\dfrac{a}{12}, \\dfrac{b}{12}\\right) = 1$ <br\/> T\u00ecm t\u00edch a.b theo c\u00f4ng th\u1ee9c \u01afCLN(a, b) . BCNN(a, b) = a. b <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm t\u00edch $\\dfrac{a}{12}. \\dfrac{b}{12}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> Vi\u1ebft t\u00edch c\u1ee7a $\\dfrac{a}{12}. \\dfrac{b}{12}$ d\u01b0\u1edbi d\u1ea1ng t\u00edch hai s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau <br\/> X\u00e9t t\u1eebng tr\u01b0\u1eddng h\u1ee3p \u0111\u1ec3 t\u00ecm a v\u00e0 b <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec \u01afCLN(a, b) = 12 $\\Rightarrow$ $\u01afCLN \\left( \\dfrac{a}{12}, \\dfrac{b}{12}\\right) = 1$ <br\/> V\u00ec a . b = \u01afCLN(a, b) . BCNN(a, b) = 336 . 12 = 4032 <br\/> $\\Rightarrow$ $\\dfrac{a}{12}. \\dfrac{b}{12} = \\dfrac{a . b}{12 . 12} = \\dfrac{4032}{144} = 28$ <br\/> M\u00e0 28 = 1 . 28 = 4 . 7 = 2 . 14 nh\u01b0ng ch\u1ec9 c\u00f3 (1, 28) = 1 v\u00e0 (4, 7) = 1 <br\/> V\u00ec a < b n\u00ean $\\dfrac{a}{12} < \\dfrac{b}{12}$ <br\/> TH1: $ \\begin{cases} \\dfrac{a}{12} = 1\\\\ \\dfrac{b}{12} = 28 \\end{cases} \\Rightarrow \\begin{cases}a = 1 . 12 = 12 \\\\ b = 28 . 12 = 336 \\end{cases}$ (lo\u1ea1i v\u00ec a > 12) <br\/> TH2: $\\begin{cases} \\dfrac{a}{12} = 4\\\\ \\dfrac{b}{12} = 7 \\end{cases} \\Rightarrow \\begin{cases}a = 4 . 12 = 48 \\\\ b = 12 . 7 = 84 \\end{cases}$ (th\u1ecfa m\u00e3n) <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: a = 48, b = 84 <\/span> "}]}],"id_ques":846},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["61"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" Ng\u01b0\u1eddi ta \u0111\u1ebfm tr\u1ee9ng trong m\u1ed9t r\u1ed5. N\u1ebfu \u0111\u1ebfm theo t\u1eebng ch\u1ee5c c\u0169ng nh\u01b0 \u0111\u1ebfm theo t\u1eebng t\u00e1 (m\u1ed9t t\u00e1 c\u00f3 12 qu\u1ea3), ho\u1eb7c \u0111\u1ebfm t\u1eebng 15 qu\u1ea3 th\u00ec l\u1ea7n n\u00e0o c\u0169ng c\u00f2n l\u1ea1i m\u1ed9t qu\u1ea3. T\u00ednh s\u1ed1 tr\u1ee9ng c\u00f3 trong r\u1ed5, bi\u1ebft s\u1ed1 tr\u1ee9ng ch\u01b0a \u0111\u1ebfn 100 qu\u1ea3. <br\/> \u0110\u00e1p s\u1ed1: _input_ qu\u1ea3 tr\u1ee9ng","hint":"N\u1ebfu s\u1ed1 tr\u1ee9ng b\u1edbt \u0111i 1 qu\u1ea3 th\u00ec chia h\u1ebft cho 10; 12 v\u00e0 15","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> N\u1ebfu g\u1ecdi s\u1ed1 tr\u1ee9ng l\u00e0 x qu\u1ea3 (x < 100) <br\/> $\\Rightarrow$ x - 1 $\\in$ BC(10; 12; 15) <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm BC(10; 12; 15) th\u00f4ng qua t\u00ecm BCNN, sau \u0111\u00f3 t\u00ecm x th\u1ecfa m\u00e3n x < 100 <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 tr\u1ee9ng c\u00f3 tr\u00f4ng r\u1ed5 l\u00e0 x qu\u1ea3 (x < 100) <br\/> V\u00ec n\u1ebfu \u0111\u1ebfm theo t\u1eebng ch\u1ee5c th\u00ec c\u00f2n 1 qu\u1ea3 n\u00ean (x - 1) $\\vdots$ 10 (1) <br\/> N\u1ebfu \u0111\u1ebfm theo t\u1eebng t\u00e1 th\u00ec th\u1eeba 1 qu\u1ea3 n\u00ean (x - 1) $\\vdots$ 12 (2) <br\/> V\u00e0 \u0111\u1ebfm t\u1eebng 15 qu\u1ea3 c\u0169ng c\u00f2n l\u1ea1i 1 qu\u1ea3 n\u00ean (x - 1) $\\vdots$ 15 (3) <br\/> T\u1eeb (1), (2) v\u00e0 (3) $\\Rightarrow$ x - 1 $\\in$ BC(10; 12; 15) <br\/> Ta c\u00f3: $10 = 2 . 5$ ; $12 = 2^2 . 3$ ; $15 = 3 . 5$ $\\Rightarrow$ BCNN(10; 12; 15) = $2^2 . 3 . 5 = 60$ <br\/> $\\Rightarrow$ (x - 1) $\\in$ BC(10; 12; 15) = {0; 60; 120; 180;...} <br\/> $\\Rightarrow$ x $\\in$ {1; 61; 121; 181;...} <br\/> V\u00ec x < 100 n\u00ean x = 61 <br\/> <span class='basic_pink'> V\u1eady trong r\u1ed5 tr\u1ee9ng c\u00f3: 61 qu\u1ea3 tr\u1ee9ng <\/span> "}]}],"id_ques":847},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" Trong m\u1ed9t h\u1ed9i ngh\u1ecb c\u00f3 500 \u0111\u1ea1i bi\u1ec3u tham d\u1ef1. M\u1ed7i \u0111\u1ea1i bi\u1ec3u c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u1ed9t trong ba th\u1ee9 ti\u1ebfng Anh, Nga v\u00e0 Ph\u00e1p. Theo th\u1ed1ng k\u00ea c\u00f3 60 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c m\u1ed9t th\u1ee9 ti\u1ebfng, 180 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Anh v\u00e0 Ph\u00e1p, 150 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c hai th\u1ee9 ti\u1ebfng Anh v\u00e0 Nga, 170 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c ti\u1ebfng Nga v\u00e0 Ph\u00e1p. H\u1ecfi c\u00f3 bao nhi\u00eau \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c c\u1ea3 3 th\u1ee9 ti\u1ebfng? <br\/> \u0110\u00e1p s\u1ed1: _input_ ng\u01b0\u1eddi","hint":"S\u1eed d\u1ee5ng s\u01a1 \u0111\u1ed3 ven","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> V\u1ebd s\u01a1 \u0111\u1ed3 ven bi\u1ec3u th\u1ecb l\u1ea1i b\u00e0i to\u00e1n <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c hai th\u1ee9 ti\u1ebfng Anh v\u00e0 Nga ho\u1eb7c Nga v\u00e0 Ph\u00e1p <br\/> 500 - (s\u1ed1 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c 1 th\u1ee9 ti\u1ebfng + s\u1ed1 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Anh v\u00e0 Ph\u00e1p) <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c c\u1ea3 3 th\u1ee9 ti\u1ebfng <br\/> S\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c c\u1ea3 3 th\u1ee9 ti\u1ebfng = (s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Anh v\u00e0 Nga + s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Nga v\u00e0 Ph\u00e1p) - s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Anh v\u00e0 Nga ho\u1eb7c Nga v\u00e0 Ph\u00e1p <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> G\u1ecdi a l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c ti\u1ebfng Nga <br\/> b l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c ti\u1ebfng Anh <br\/> c l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c ti\u1ebfng Ph\u00e1p <br\/> d l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c hai th\u1ee9 ti\u1ebfng Anh v\u00e0 Ph\u00e1p $\\Rightarrow$ d = 180 <br\/> e l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c hai th\u1ee9 ti\u1ebfng Nga v\u00e0 Ph\u00e1p $\\Rightarrow$ e = 170 <br\/> g l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Anh v\u00e0 Nga $\\Rightarrow$ g = 150 <br\/> h l\u00e0 s\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c c\u1ea3 3 th\u1ee9 ti\u1ebfng <br\/> V\u1eady ta c\u00f3 s\u01a1 \u0111\u1ed3: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai17/lv3/img\/D6117_K101.png' \/><\/center> <br\/> Theo b\u00e0i ra ta c\u00f3: a + b + c = 60 <br\/> D\u1ef1a v\u00e0o s\u01a1 \u0111\u1ed3 ta c\u00f3: <br\/> S\u1ed1 \u0111\u1ea1i bi\u1ec3u ch\u1ec9 n\u00f3i \u0111\u01b0\u1ee3c 2 th\u1ee9 ti\u1ebfng Anh v\u00e0 Nga ho\u1eb7c Nga v\u00e0 ph\u00e1p l\u00e0: <br\/> 500 - (60 + 180) = 260 (ng\u01b0\u1eddi) <br\/> S\u1ed1 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c c\u1ea3 3 th\u1ee9 ti\u1ebfng l\u00e0: <br\/> (170 + 150) - 260 = 60 (ng\u01b0\u1eddi) <br\/> V\u1eady c\u00f3 60 \u0111\u1ea1i bi\u1ec3u n\u00f3i \u0111\u01b0\u1ee3c c\u1ea3 3 th\u1ee9 ti\u1ebfng<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 60 <\/span> "}]}],"id_ques":848},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" T\u00ecm ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a s\u1ed1 $19^{2008}$<br\/> \u0110\u00e1p \u00e1n l\u00e0: _input_ ","hint":"T\u00ecm ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $9^{2008}$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ecm ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $9^{2008}$ <br\/> V\u00ec $9^2$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 n\u00ean vi\u1ebft 2008 th\u00e0nh t\u00edch c\u1ee7a 2 v\u00e0 1 s\u1ed1 <br\/> 1 n\u00e2ng l\u00ean l\u0169y th\u1eeba bao nhi\u00eau c\u0169ng v\u1eabn b\u1eb1ng 1 n\u00ean $9^{2008}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0... <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $19^{2008}$ <br\/> Ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $19^{2008}$ ch\u00ednh l\u00e0 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $9^{2008}$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $19^{2008}$ ch\u00ednh l\u00e0 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $9^{2008}$ <br\/> Ta c\u00f3: $9^2$ = 81 c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 <br\/> M\u00e0 $9^{2008} = 9^{2 . 1004} = (9^2)^{1004}$ n\u00ean $9^{2008}$ s\u1ebd c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng c\u1ee7a $1^{1004}$ <br\/> 1 n\u00e2ng l\u00ean l\u0169y th\u1eeba bao nhi\u00eau c\u0169ng b\u1eb1ng 1 n\u00ean $1^{1004}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 <br\/> $\\Rightarrow$ $9^{2008}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 <br\/> $\\Rightarrow$ $19^{2008}$ c\u00f3 ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng l\u00e0 1 <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 1 <\/span> "}]}],"id_ques":849},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["53784"]]],"list":[{"point":10,"width":80,"type_input":"","ques":" Thay x, y b\u1eb1ng ch\u1eef s\u1ed1 th\u00edch h\u1ee3p \u0111\u1ec3 $\\overline{x378y}$ chia h\u1ebft cho 72 <br\/> Sau khi thay x, y v\u00e0o ta \u0111\u01b0\u1ee3c s\u1ed1: _input_ ","hint":"Vi\u1ebft 72 = a . b; (a, b) = 1 <br\/> $\\overline{x378y}$ $\\vdots$ 72 khi $\\overline{x378y}$ $\\vdots$ a v\u00e0 $\\overline{x378y}$ $\\vdots$ b","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Vi\u1ebft 72 th\u00e0nh t\u00edch hai s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau <br\/> 72 = 8 . 9; (8, 9) = 1 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Ta \u0111i t\u00ecm y th\u1ecfa m\u00e3n $\\overline{x378y}$ $\\vdots$ 8 <br\/> $\\overline{x378y}$ $\\vdots$ 8 khi $\\overline{78y}$ $\\vdots$ 8 <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay y v\u00e0o r\u1ed3i t\u00ecm x th\u1ecfa m\u00e3n $\\overline{x378y}$ $\\vdots$ 9 <br\/> $\\overline{x378y}$ $\\vdots$ 9 khi t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 chia h\u1ebft cho 9 <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: 72 = 8 . 9 m\u00e0 (8, 9) = 1 <br\/> N\u00ean \u0111\u1ec3 $\\overline{x378y}$ $\\vdots$ 72 th\u00ec $\\overline{x378y}$ $\\vdots$ 8 v\u00e0 $\\overline{x378y}$ $\\vdots$ 9 <br\/> \u0110\u1ec3 $\\overline{x378y}$ $\\vdots$ 8 th\u00ec ba ch\u1eef s\u1ed1 t\u1eadn c\u00f9ng $\\overline{78y}$ ph\u1ea3i l\u00e0 s\u1ed1 chia h\u1ebft cho 8 <br\/> $\\Rightarrow$ y = 4 thay y = 4 v\u00e0o ta \u0111\u01b0\u1ee3c $\\overline{x3784}$ <br\/> C\u1ea7n t\u00ecm x \u0111\u1ec3 $\\overline{x3784}$ $\\vdots$ 9 <br\/> \u0110\u1ec3 $\\overline{x3784}$ $\\vdots$ 9 th\u00ec t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1: x + 3 + 7 + 8 + 4 = 22 + x $\\vdots$ 9 <br\/> (22 + x) $\\vdots$ 9 khi x = 5 <br\/> Thay x = 5 v\u00e0o ta \u0111\u01b0\u1ee3c s\u1ed1 53784 <br\/> Ta c\u00f3 53784 $\\vdots$ 8 v\u00e0 53784 $\\vdots$ 9 $\\Rightarrow$ 53784 $\\vdots$ 72 <b> (th\u1ecfa m\u00e3n) <\/b> <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 53784 <\/span> "}]}],"id_ques":850}],"lesson":{"save":0,"level":3}}