Câu hỏi của Thai Nguyen

Question

Tính giá trị biểu thức:

$A=4\sqrt{80\sqrt{7}}-2\sqrt{45\sqrt{7}}-5\sqrt{20\sqrt{7}}$

$B=\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}$

Nhã Doanh · Accepted Answer

*$A=2\sqrt{80\sqrt{7}}-2\sqrt{45\sqrt{7}}-5\sqrt{20\sqrt{7}}$

$A=16\sqrt{5\sqrt{7}}-6\sqrt{5\sqrt{7}}-10\sqrt{5\sqrt{7}}$

$A=\left(16-6-10\right)\sqrt{5\sqrt{7}}=0$

* $B=\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}$

$B^3=5+2\sqrt{13}+5-2\sqrt{13}+3\left(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\right).\sqrt[3]{\left(5+2\sqrt{13}\right)\left(5-2\sqrt{13}\right)}$

$B^3=10-9B$

$\Rightarrow B^3+9B-10=0$

$\Rightarrow B^3-B^2+B^2-B+10B-10=0$

$\Rightarrow B^2\left(B-1\right)+B\left(B-1\right)+10\left(B-1\right)=0$

$\Rightarrow\left(B-1\right)\left(B^2+B+10\right)=0$

$\Rightarrow B=1$Câu trả lời: *$A=2\sqrt{80\sqrt{7}}-2\sqrt{45\sqrt{7}}-5\sqrt{20\sqrt{7}}$