Câu hỏi của Vy Nguyễn Đặng Khánh

Question

Thu gọn biểu thức sau:

E= ($\left(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\right)^2$

Y · Accepted Answer

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

$E=\left(\sqrt{\frac{\left(\sqrt{5}+1\right)^2}{2}}-\sqrt{\frac{\left(\sqrt{5}-1\right)^2}{2}}\right)^2$

$E=\left[\frac{1}{\sqrt{2}}\left(\sqrt{5}+1-\sqrt{5}+1\right)\right]^2$

$E=\left(\frac{1}{\sqrt{2}}\cdot2\right)^2=\sqrt{2}^2=2$Câu trả lời: $E=\left(\sqrt{\frac{6+2\sqrt{5}}{2}}-\sqrt{\frac{6-2\sqrt{5}}{2}}\right)^2$

$E=\left(\sqrt{\frac{\left(\sqrt{5}+1\right)^2}{2}}-\sqrt{\frac{\left(\sqrt{5}-1\right)^2}{2}}\right)^2$

$E=\left[\frac{1}{\sqrt{2}}\left(\sqrt{5}+1-\sqrt{5}+1\right)\right]^2$

$E=\left(\frac{1}{\sqrt{2}}\cdot2\right)^2=\sqrt{2}^2=2$

Bài 1: Căn bậc hai