Question

поривняйте числа a и b якщо a=11√6+√24-2√54
b=7√5-√45 +√80​

Answer 1

$a=11sqrt{6}+sqrt{24}-2sqrt{54}=11sqrt{6} +sqrt{4*6}-2sqrt{9*6} =11sqrt{6} +2sqrt{6} -6sqrt{6}=7sqrt{6}=sqrt{7^{2}*6 }=sqrt{49*6}=sqrt{294}\\b=7sqrt{5}-sqrt{45}+sqrt{80}=7sqrt{5}-sqrt{9*5}+sqrt{16*5}=7sqrt{5} -3sqrt{5}+4sqrt{5} =8sqrt{5}=sqrt{8^{2}*5 }=sqrt{64*5}=sqrt{320} \\sqrt{294} <sqrt{320} \\a<b$