Câu hỏi của Sonyeondan Bangtan

Question

Tính:

a) $\left(\sqrt{7}-\sqrt{5}+\sqrt{2}\right)$$\left(\sqrt{2}-\sqrt{7}-\sqrt{5}\right)$

b) $\sqrt{2}\cdot\sqrt{2+\sqrt{3}}$

c) $\left(\sqrt{2}-\sqrt{6}\right)$$\sqrt{2+\sqrt{3}}$

Trần Thanh Phương · Accepted Answer

a) $\left(\sqrt{7}-\sqrt{5}+\sqrt{2}\right)\left(\sqrt{2}-\sqrt{7}-\sqrt{5}\right)$

$=\left[\left(\sqrt{2}-\sqrt{5}\right)+\sqrt{7}\right]\left[\left(\sqrt{2}-\sqrt{5}\right)-\sqrt{7}\right]$

$=\left(\sqrt{2}-\sqrt{5}\right)^2-\left(\sqrt{7}\right)^2$

$=2-2\sqrt{10}+5-7$

$=-2\sqrt{10}$

b) $\sqrt{2}\cdot\sqrt{2+\sqrt{3}}$

$=\sqrt{4+2\sqrt{3}}$

$=\sqrt{\left(\sqrt{3}+1\right)^2}$

$=\sqrt{3}+1$

c) $\left(\sqrt{2}-\sqrt{6}\right)\sqrt{2+\sqrt{3}}$

$=\sqrt{2}\cdot\left(1-\sqrt{3}\right)\cdot\sqrt{2+\sqrt{3}}$

$=\left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)$

$=1-3$

$=-2$Câu trả lời: a) $\left(\sqrt{7}-\sqrt{5}+\sqrt{2}\right)\left(\sqrt{2}-\sqrt{7}-\sqrt{5}\right)$

$=\left[\left(\sqrt{2}-\sqrt{5}\right)+\sqrt{7}\right]\left[\left(\sqrt{2}-\sqrt{5}\right)-\sqrt{7}\right]$

$=\left(\sqrt{2}-\sqrt{5}\right)^2-\left(\sqrt{7}\right)^2$

$=2-2\sqrt{10}+5-7$

$=-2\sqrt{10}$

b) $\sqrt{2}\cdot\sqrt{2+\sqrt{3}}$

$=\sqrt{4+2\sqrt{3}}$

$=\sqrt{\left(\sqrt{3}+1\right)^2}$

$=\sqrt{3}+1$

c) $\left(\sqrt{2}-\sqrt{6}\right)\sqrt{2+\sqrt{3}}$

$=\sqrt{2}\cdot\left(1-\sqrt{3}\right)\cdot\sqrt{2+\sqrt{3}}$

$=\left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)$

$=1-3$

$=-2$

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