Question

Rút gọn biểu thức
A= \(\frac{\left(2+\sqrt{3}\right)\left(\sqrt{2-\sqrt{3}}\right)}{\sqrt{2+\sqrt{3}}}\)

Answer 1

A= \(\frac{\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}} \)
A= \(\frac{\left(2+\sqrt{3}\right)\left(\sqrt{2-\sqrt{3}}\right)\left(\sqrt{2-\sqrt{3}}\right)}{\left(\sqrt{2+\sqrt{3}}\right)\left(\sqrt{2-\sqrt{3}}\right)}\)
A=\(\frac{\left(2+\sqrt{3}\right)\left[\left(\sqrt{2-\sqrt{3}}\right)\right]^2}{1}\)
A=\(\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\)
A=2² - (\(\sqrt{3}\))^{2
A= 1
Vậy A = 1}