Question

[chi mai Nguyen]

\(A=\left(\sqrt{3}+1\right)^2+\frac{5}{4}\sqrt{48}-\frac{2}{\sqrt{3}+1}\)
\(B=\frac{4}{3-\sqrt{5}}-\frac{3}{\sqrt{5}+\sqrt{2}}-\frac{1}{\sqrt{2}-1}\)

\(C=\sqrt{4-2\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)

Rút gọn biểu thức 

Giúp mình với mình cần gấp

Answer 1

[Nguyễn Việt Hoàng]

\(C=\sqrt{4-2\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)

\(\Leftrightarrow C=\sqrt{3-2\sqrt{3}+1}-\sqrt{4+4\sqrt{3}+3}\)

\(\Leftrightarrow C=\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2+\sqrt{3}\right)^2}\)

\(\Leftrightarrow C=\left|\sqrt{3}-1\right|-\left|2+\sqrt{3}\right|\)

\(\Leftrightarrow C=\sqrt{3}-1-2-\sqrt{3}\)

\(\Leftrightarrow C=-3\)