Question

rút gọn biểu thức sau

B=\(\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}-\dfrac{1}{\sqrt{5}+\sqrt{2}}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)

Answer 1

\(B=\left(\dfrac{\sqrt{5}+\sqrt{2}}{5-2}-\dfrac{\sqrt{5}-\sqrt{2}}{5-2}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\\ =\left(\dfrac{\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}}{3}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\\ =\left(\dfrac{2\sqrt{2}}{3}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\\ =\dfrac{2\sqrt{2}+3}{3}.\dfrac{1}{\left(\sqrt{2}+1\right)^2}\\ =\dfrac{\left(\sqrt{2}+1\right)^2}{3\left(\sqrt{2}+1\right)^2}\\ =\dfrac{1}{3}\)