Question

tính :\(\dfrac{1}{\sqrt{\dfrac{9}{4}+\sqrt{5}}}\)-\(\dfrac{1}{\sqrt{\dfrac{9}{4}-\sqrt{5}}}\)

Answer 1

\(A=\dfrac{1}{\sqrt{\dfrac{9}{4}+\sqrt{5}}}-\dfrac{1}{\sqrt{\dfrac{9}{4}-\sqrt{5}}}\)

\(=\dfrac{1}{\sqrt{\dfrac{5}{4}+2.\sqrt{\dfrac{5}{4}}+1}}-\dfrac{1}{\sqrt{\dfrac{5}{4}-2.\sqrt{\dfrac{5}{4}}+1}}\)

\(=\dfrac{1}{\sqrt{\left(\sqrt{\dfrac{5}{4}}+1\right)^2}}-\dfrac{1}{\sqrt{\left(\sqrt{\dfrac{5}{4}}-1\right)^2}}\)

\(=\dfrac{1}{\sqrt{\dfrac{5}{4}}+1}-\dfrac{1}{\sqrt{\dfrac{5}{4}}-1}=\dfrac{\sqrt{\dfrac{5}{4}}-1-\sqrt{\dfrac{5}{4}}-1}{\dfrac{5}{4}-1}\)

\(=\dfrac{-2}{\dfrac{1}{4}}=-8\)