Question

rút gọn biểu thức:

\(\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}\)

Answer 1

Lời giải:

Đặt \(\sqrt{\sqrt{3}+1}=a\Rightarrow \sqrt{3}=a^2-1\)

\(\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}=\frac{a^2-1}{a-1}-\frac{a^2-1}{a+1}\)

\(=\frac{(a-1)(a+1)}{a-1}-\frac{(a-1)(a+1)}{a+1}=(a+1)-(a-1)=2\)

Answer 2

\(=\sqrt{3}\left[\frac{\sqrt{\sqrt{3}+1}+1-\sqrt{\sqrt{3}+1}+1}{\sqrt{3}+1-1}\right]\)

\(=\sqrt{3}.\frac{2}{\sqrt{3}}=2\)