Câu hỏi của Trịnh Long

Question

Rút gọn

$\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{18}}$

$\left(\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\right).\left(15+2\sqrt{6}\right)$

Nguyễn Lê Phước Thịnh · Accepted Answer

b) Ta có: $\left(\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\right)\cdot\left(15+2\sqrt{6}\right)$

$=\left(\frac{5+2\sqrt{6}+2\left(5-2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)}\right)\cdot\left(15+2\sqrt{6}\right)$

$=\frac{5+2\sqrt{6}+10-4\sqrt{6}}{25-24}\cdot\left(15+2\sqrt{6}\right)$

$=\left(15-2\sqrt{6}\right)\cdot\left(15+2\sqrt{6}\right)$

$=15^2-\left(2\sqrt{6}\right)^2$

$=225-24=201$Câu trả lời: b) Ta có: $\left(\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\right)\cdot\left(15+2\sqrt{6}\right)$

$=\left(\frac{5+2\sqrt{6}+2\left(5-2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)}\right)\cdot\left(15+2\sqrt{6}\right)$

$=\frac{5+2\sqrt{6}+10-4\sqrt{6}}{25-24}\cdot\left(15+2\sqrt{6}\right)$

$=\left(15-2\sqrt{6}\right)\cdot\left(15+2\sqrt{6}\right)$

$=15^2-\left(2\sqrt{6}\right)^2$

$=225-24=201$

Bài 3: Liên hệ giữa phép nhân và phép khai phương