Bất phương trình bậc nhất hai ẩn

Home Lớp 10 Toán lớp 10 - Sách Kết nối tri thức Bài 3: Bất phương trình bậc nhất hai ẩnBài tập nâng cao

{"common":{"save":0,"post_id":"6076","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5307","mon_id":"1158767","chapter_id":"1158774","post_id":"6076","question":"M\u1ed9t c\u1eeda hàng bán l\u1ebb bán hai lo\u1ea1i h\u1ea1t cà phê. Lo\u1ea1i th\u1ee9 nh\u1ea5t giá 150 nghìn \u0111\u1ed3ng\/kg và lo\u1ea1i th\u1ee9 hai giá 200 nghìn \u0111\u1ed3ng\/kg. C\u1eeda hàng tr\u1ed9n <\/span>x<\/strong><\/span> kg lo\u1ea1i th\u1ee9 nh\u1ea5t và <\/span>y<\/strong><\/span> kg lo\u1ea1i th\u1ee9 hai sao cho h\u1ea1t cà phê \u0111ã tr\u1ed9n có giá không quá 180 nghìn \u0111\u1ed3ng\/kg.<\/span><\/p>L\u1eadp b\u1ea5t ph\u01b0\u01a1ng trình b\u1eadc nh\u1ea5t hai \u1ea9n th\u1ecfa mãn \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec1 bài.<\/span><\/p>","options":["A.<\/strong> $3x-2y \\ge 0$<\/span>","B.<\/strong> $150x + 200y \\ge 180(x + y)$<\/span>","C.<\/strong> $150x + 200y \\le 180x + y$<\/span>","D.<\/strong> $3x + 2y \\le 0$<\/span>"],"correct":"1","level":"3","hint":"","answer":"S\u1ed1 ti\u1ec1n c\u1ee7a <\/span>x<\/span><\/strong> kg cà phê lo\u1ea1i th\u1ee9 nh\u1ea5t là <\/span>150x<\/strong> <\/span>(nghìn \u0111\u1ed3ng).<\/span><\/p>S\u1ed1 ti\u1ec1n c\u1ee7a<\/span> y<\/strong> <\/span>kg cà phê lo\u1ea1i th\u1ee9 hai là <\/span>20<\/span><\/strong>0y<\/strong> <\/span>(nghìn \u0111\u1ed3ng).<\/span><\/p>T\u1ed5ng s\u1ed1 ti\u1ec1n khi tr\u1ed9n <\/span>x<\/span> kg lo\u1ea1i th\u1ee9 nh\u1ea5t và <\/span>y<\/span> kg lo\u1ea1i th\u1ee9 hai là: <\/span>150x + 200y<\/span><\/strong> (nghìn \u0111\u1ed3ng).<\/span><\/p>T\u1ed5ng s\u1ed1 kg cà phê sau khi tr\u1ed9n <\/span>x<\/span> kg lo\u1ea1i th\u1ee9 nh\u1ea5t và <\/span>y<\/span> kg lo\u1ea1i th\u1ee9 hai là: <\/strong><\/span>x + y<\/span><\/strong> (kg).<\/span><\/p>Vì cà phê sau khi tr\u1ed9n có giá không quá <\/span>180<\/span> nghìn \u0111\u1ed3ng\/kg nên s\u1ed1 ti\u1ec1n cao nh\u1ea5t thu \u0111\u01b0\u1ee3c khi bán <\/span>x + y<\/span> kg cà phê là <\/span>180(x + y) <\/span>(nghìn \u0111\u1ed3ng).<\/span><\/p>Khi \u0111ó ta có b\u1ea5t ph\u01b0\u01a1ng trình <\/span><\/p>                                $150x+200y \\le 180(x+y)$<\/span><\/span><\/p>⇔                             $150x+200y \\le 180x + 180y$<\/span><\/span><\/p>⇔ $150x + 200 y - 180x - 180 y \\le 0$<\/span><\/span><\/p>⇔                              $-30x+20y \\le 0$<\/span><\/span><\/p>⇔                                      $3x-2y \\ge 0$<\/span><\/span><\/p>V\u1eady b\u1ea5t ph\u01b0\u01a1ng trình b\u1eadc nh\u1ea5t hai \u1ea9n x, y th\u1ecfa mãn \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec1 bài là  $3x - 2y \\ge 0$<\/span> .<\/span><\/p>\u0110áp án \u0111úng là    <\/span>A.<\/strong> $3x-2y \\ge 0$<\/span><\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2022-09-02 02:33:49","option_type":"math","len":0},{"id":"5310","mon_id":"1158767","chapter_id":"1158774","post_id":"6076","question":"Giá ti\u1ec1n m\u1ed9t lo\u1ea1i v\u1edf 200 trang là 18 nghìn \u0111\u1ed3ng và giá ti\u1ec1n m\u1ed9t lo\u1ea1i v\u1edf 100 trang là 9 nghìn \u0111\u1ed3ng. M\u1eb9 cho Trang 210 nghìn \u0111\u1ed3ng \u0111\u1ec3 mua v\u1edf m\u1edbi. G\u1ecdi x, y l\u1ea7n l\u01b0\u1ee3t là s\u1ed1 quy\u1ec3n v\u1edf 200 trang và s\u1ed1 quy\u1ec3n v\u1edf 100 trang mà Trang s\u1ebd mua. Vi\u1ebft b\u1ea5t ph\u01b0\u01a1ng trình b\u1eadc nh\u1ea5t hai \u1ea9n bi\u1ec3u th\u1ecb m\u1ed1i liên h\u1ec7 gi\u1eefa x và y sao cho t\u1ed5ng s\u1ed1 ti\u1ec1n Trang ph\u1ea3i tr\u1ea3 không v\u01b0\u1ee3t quá s\u1ed1 ti\u1ec1n m\u1eb9 cho.<\/span><\/p>","options":["A.<\/strong> $18x + 9y \\ge 210$<\/span>","B.<\/strong> $18x - 9y \\le 210$<\/span>","C.<\/strong> $6x + 9y \\ge 210$<\/span>","D.<\/strong> $6x + 3y \\le 70$<\/span>"],"correct":"4","level":"3","hint":"","answer":"S\u1ed1 ti\u1ec1n Trang ph\u1ea3i tr\u1ea3 khi mua <\/span>x<\/strong><\/span> quy\u1ec3n v\u1edf 200 trang là <\/span>18x<\/span> nghìn \u0111\u1ed3ng.<\/span><\/p>S\u1ed1 ti\u1ec1n Trang<\/span> ph\u1ea3i tr\u1ea3 khi mua <\/span>y<\/strong><\/span> quy\u1ec3n v\u1edf 100 trang là<\/span> 9y <\/span> nghìn \u0111\u1ed3ng.<\/span><\/p>T\u1ed5ng s\u1ed1 ti\u1ec1n Trang<\/span> ph\u1ea3i tr\u1ea3 là <\/span>18x + 9y  <\/span>nghìn \u0111\u1ed3ng.<\/span><\/p>Vì s\u1ed1 ti\u1ec1n Trang<\/span> dùng \u0111\u1ec3 mua v\u1edf không \u0111\u01b0\u1ee3c v\u01b0\u1ee3t quá s\u1ed1 ti\u1ec1n mà m\u1eb9 cho là 210 nghìn \u0111\u1ed3ng nên ta có b\u1ea5t ph\u01b0\u01a1ng trình:<\/span><\/p>   $18x + 9y \\le 210$<\/span><\/span><\/p>⇔   $6x + 3y \\le 70$<\/span><\/span><\/p>V\u1eady b\u1ea5t ph\u01b0\u01a1ng trình c\u1ea7n tìm là  <\/span>D.<\/strong><\/span> <\/span>$6x + 3y \\le 70$<\/span><\/span> <\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2022-09-02 03:31:02","option_type":"math","len":0},{"id":"5317","mon_id":"1158767","chapter_id":"1158774","post_id":"6076","question":"Cho b\u1ea5t ph\u01b0\u01a1ng trình  $-2x + \\sqrt{3} y + \\sqrt{2} \\le 0$<\/span>   có t\u1eadp nghi\u1ec7m là S. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là kh\u1eb3ng \u0111\u1ecbnh \u0111úng<\/strong>?<\/p>","options":["A.<\/strong> (1 ; 1) ∈ S","B.<\/strong> $\\left( \\dfrac{\\sqrt{2}}{2} ; 0 \\right)$<\/span> ∈ S","C.<\/strong> (1 ; –2) ∉ S","D.<\/strong> (1 ; 0) ∉ S"],"correct":"2","level":"3","hint":"","answer":"A.<\/strong> (1 ; 1) ∈ S  (sai<\/span>, vì  $-2.1 + \\sqrt{3} .1 + \\sqrt{2} \\le 0$<\/span>  là b\u1ea5t \u0111\u1eb3ng th\u1ee9c sai nên (1 ; 1) ∉ S)<\/p>B.<\/strong> $\\left( \\dfrac{\\sqrt{2}}{2} ; 0 \\right)$<\/span> ∈ S  (\u0111úng<\/span>, vì  $-2.\\dfrac{\\sqrt{2}}{2} + \\sqrt{3} . 0 + \\sqrt{2} \\le 0$<\/span>  là b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111úng)<\/p>C.<\/strong> (1 ; –2) ∉ S   (sai<\/span>, vì  $-2 . 1 + \\sqrt{3} . (-2) + \\sqrt{2} \\le 0$<\/span>  là b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111úng nên (1; –2) ∈ S)<\/p>D.<\/strong> (1 ; 0) ∉ S   (sai<\/span>, vì $-2.1 + \\sqrt{3} . 0 + \\sqrt{2} \\le 0$<\/span>  là b\u1ea5t \u0111\u1eb3ng th\u1ee9c \u0111úng nên (1; 0) ∈ S)<\/p>\u0110áp án \u0111úng là   B.<\/strong> $\\left( \\dfrac{\\sqrt{2}}{2} ; 0 \\right)$<\/span> ∈ S<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2022-09-02 04:58:13","option_type":"math","len":0}]}