Question

\(\frac{1}{\sqrt{7-\sqrt{24}}+1}+\frac{1}{\sqrt{7+\sqrt{24}}+1}\) 

Rút gọn

Answer 1

\(\sqrt{7+\sqrt{24}=\sqrt{7+2\sqrt{6}}=\sqrt{\left(\sqrt{6}+1\right)^2}}\)

Answer 2

mình cũng làm vậy nhưng ko ra kết quả 

Answer 3

\(\frac{1}{\sqrt{7-\sqrt{24}}+1}+\frac{1}{\sqrt{7+\sqrt{24}}+1}\)

\(=\frac{1}{\sqrt{7-2\sqrt{6}}+1}+\frac{1}{\sqrt{7+2\sqrt{6}}+1}\)

\(=\frac{1}{\sqrt{\left(\sqrt{6}-1\right)^2}+1}+\frac{1}{\sqrt{\left(\sqrt{6}+1\right)^2}+1}\)

\(=\frac{1}{\sqrt{6}-1+1}+\frac{1}{\sqrt{6}+1+1}\)

\(=\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{6}+2}=\frac{\sqrt{6}+2+\sqrt{6}}{6+2\sqrt{6}}=\frac{2\sqrt{6}+2}{6+2\sqrt{6}}\)