Question

Cho x= \(\dfrac{\sqrt{13-4\sqrt{3}}}{2}.Tính\)  A = \(\dfrac{\sqrt{x}+2}{2\sqrt{x}-3}\)

Answer 1

Lời giải:
\(x=\frac{\sqrt{13-4\sqrt{3}}}{2}=\frac{\sqrt{13-2\sqrt{12}}}{2}=\frac{\sqrt{12+1-2\sqrt{12}}}{2}=\frac{\sqrt{(\sqrt{12}-1)^2}}{2}=\frac{\sqrt{12}-1}{2}\)

\(2A=1+\frac{7}{2\sqrt{x}-3}=1+\frac{7}{\sqrt{2\sqrt{12}-2}}\)

\(A=\frac{1}{2}+\frac{7}{2\sqrt{4\sqrt{3}-2}}\)