{"common":{"save":0,"post_id":"7834","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7726","post_id":"7834","mon_id":"1159278","chapter_id":"1159327","question":"<p>\u0110i\u1ec1n vào ch\u1ed7 ch\u1ea5m: <span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}$<\/span> ... <span class=\"math-tex\">$\\sqrt{21}$<\/span>.<\/p>","options":["<strong>A.<\/strong> ≤","<strong>B.<\/strong> =","<strong>C.<\/strong> ≥","<strong>D.<\/strong> >"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> ≤<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}<\\dfrac{30-2\\sqrt{36}}{4}=\\dfrac{30-2.6}{4}=4,5=\\sqrt{20,25}<\\sqrt{21}$<\/span><\/p><p>Do \u0111ó <span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}$<\/span> < <span class=\"math-tex\">$\\sqrt{21}$<\/span> hay <span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}$<\/span> <span style=\"color:#16a085;\">≤<\/span> <span class=\"math-tex\">$\\sqrt{21}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-13 04:00:52","option_type":"txt","len":0},{"id":"7727","post_id":"7834","mon_id":"1159278","chapter_id":"1159327","question":"<p>Trong các h\u1ec7 th\u1ee9c sau \u0111ây, h\u1ec7 th\u1ee9c nào <strong>\u0111úng <\/strong>v\u1edbi m\u1ecdi s\u1ed1 d\u01b0\u01a1ng a và b?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}=\\sqrt{a}+\\sqrt{b}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}>\\sqrt{a}+\\sqrt{b}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}<\\sqrt{a}+\\sqrt{b}$<\/span>","<strong>D.<\/strong> C\u1ea3 ba \u0111áp án trên."],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}<\\sqrt{a}+\\sqrt{b}$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$(\\sqrt{a+b})^2=a+b$<\/span> (1)<\/p><p><span class=\"math-tex\">$(\\sqrt{a}+\\sqrt{b})^2=a+b+2\\sqrt{ab}$<\/span> (2)<\/p><p>T\u1eeb (1) và (2) suy ra \u0111áp án A, B \u0111\u1ec1u sai.<\/p><p>Do <span class=\"math-tex\">$a+b< a+b+2\\sqrt{ab}$<\/span> suy ra <span class=\"math-tex\">$0< \\sqrt{ab}$<\/span> (\u0111úng v\u1edbi m\u1ecdi s\u1ed1 d\u01b0\u01a1ng a, b).<\/p><p>V\u1eady C \u0111úng.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-13 04:05:23","option_type":"math","len":0},{"id":"7728","post_id":"7834","mon_id":"1159278","chapter_id":"1159327","question":"<p>Cho bi\u1ec3u th\u1ee9c <span class=\"math-tex\">$A=\\sqrt[3]{2+\\sqrt{5}}$<\/span>. Tính B = A³ – 1.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$B=1-\\sqrt{5}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$B=2+\\sqrt{5}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$B=\\sqrt{5}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$B=1+\\sqrt{5}$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$B=1+\\sqrt{5}$<\/span><\/span><\/p><p>B = A³ – 1 = <span class=\"math-tex\">$(\\sqrt[3]{2+\\sqrt{5}})^3-1$<\/span> = <span class=\"math-tex\">$2+\\sqrt{5}-1=1+\\sqrt{5}$<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-13 04:09:24","option_type":"math","len":0}]}
