Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"7304","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7520","mon_id":"1158767","chapter_id":"1159257","post_id":"7304","question":"<p>Cho a, b, c > 0 là \u0111\u1ed9 dài ba c\u1ea1nh c\u1ee7a m\u1ed9t tam giác. M\u1ec7nh \u0111\u1ec1 nào <strong>sai<\/strong>?<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$a^2 < ab + ac$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$a^2+c^2 < b^2+ 2ac$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$b^2+c^2 > a^2+ 2bc$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$ab+bc> b^2$<\/span>"],"correct":"3","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <\/strong><span class=\"math-tex\">$b^2+c^2 > a^2+ 2bc$<\/span><\/span><\/p><p>Vì <span class=\"math-tex\">$b^2+c^2-a^2=2bc.\\cos A < 2bc$<\/span> ⇒ <span class=\"math-tex\">$b^2+c^2 < a^2+ 2bc$<\/span> nên câu <span style=\"color:#16a085;\">C sai.<\/span><\/p><p>Vì <span class=\"math-tex\">$a^2+c^2-b^2=2ac.\\cos B \\le 2ac$<\/span> ⇒ <span class=\"math-tex\">$a^2+c^2 < b^2+ 2ac$<\/span> nên câu <span style=\"color:#e74c3c;\">B \u0111úng<\/span><span style=\"color:#16a085;\">.<\/span><\/p><p>Áp d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c trong tam giác, ta có<\/p><p><span class=\"math-tex\">$a< b+ c $<\/span> ⇒ <span class=\"math-tex\">$a^2 < ab + ac$<\/span> nên câu <span style=\"color:#e74c3c;\">A \u0111úng<\/span>.<\/p><p><span class=\"math-tex\">$a + c > b $<\/span> ⇒ <span class=\"math-tex\">$ab+bc> b^2$<\/span> nên câu <span style=\"color:#e74c3c;\">D \u0111úng<\/span>. <\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 04:36:59","option_type":"math","len":0},{"id":"7522","mon_id":"1158767","chapter_id":"1159257","post_id":"7304","question":"<p>Cho tam giác ABC có AB = 4cm, BC = 7cm, AC = 9cm. Tính cos A.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\cos A=-\\dfrac{2}{3}$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\cos A=\\dfrac{1}{2}$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$\\cos A=\\dfrac{1}{3}$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$\\cos A=\\dfrac{2}{3}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D. <\/strong><span class=\"math-tex\">$\\cos A=\\dfrac{2}{3}$<\/span><\/span><\/p><p>Ta có:<\/p><p><span class=\"math-tex\">$\\cos A=\\dfrac{AB^2+AC^2-BC^2}{2.AB.AC}=\\dfrac{4^2+9^2-7^2}{2.4.9}=\\dfrac{2}{3}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 04:43:00","option_type":"math","len":0},{"id":"7524","mon_id":"1158767","chapter_id":"1159257","post_id":"7304","question":"<p>Cho tam giác ABC có <span class=\"math-tex\">$a^2+b^2-c^2 > 0$<\/span>. Khi \u0111ó:<\/p><p><span class=\"svgedit\"><svg height=\"200\" width=\"320\"> <g><title><\/title><rect fill=\"#fff\" height=\"202\" id=\"canvas_background\" width=\"322\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_8\"> <path d=\"m90.7405,28.27586l204,142l-272,-1z\" fill=\"#ffffaa\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"80.89999\" xml:space=\"preserve\" y=\"22.45\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"1.9\" xml:space=\"preserve\" y=\"181.45\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"300.89999\" xml:space=\"preserve\" y=\"178.45\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Georgia, Times, Times New Roman, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"135.89999\" xml:space=\"preserve\" y=\"192.45\">a<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Georgia, Times, Times New Roman, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"192.89999\" xml:space=\"preserve\" y=\"91.45\">b<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Georgia, Times, Times New Roman, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"37.89999\" xml:space=\"preserve\" y=\"107.45\">c<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\widehat{C} > 90^o$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\widehat{C} < 90^o$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$\\widehat{C} = 90^o$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$\\widehat{C} = 120^o$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <\/strong><span class=\"math-tex\">$\\widehat{C} < 90^o$<\/span><\/span><\/p><p>Vì <span class=\"math-tex\">$a^2+b^2-c^2 > 0$<\/span> nên <span class=\"math-tex\">$\\cos C=\\dfrac{a^2+b^2-c^2}{2ab} > 0$<\/span> suy ra <span style=\"color:#16a085;\"><span class=\"math-tex\">$\\widehat{C} < 90^o$<\/span><\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 04:49:07","option_type":"math","len":0}]}