Question

Cho A=(\(\dfrac{\sqrt{a}-2}{a-1}-\dfrac{\sqrt{a}+2}{a+2\sqrt{a}+1}\)).\(\dfrac{\left(1-a\right)^2}{2}\)

a) Rút gọn Biểu thức A

b) tìm GTLN của A

Answer 1

a: \(A=\left(\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)-\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)}\right)\cdot\dfrac{\left(a-1\right)^2}{2}\)

\(=\dfrac{a-\sqrt{a}-2-a-\sqrt{a}+2}{1}\cdot\dfrac{\sqrt{a}-1}{2}\)

\(=-\sqrt{a}\left(\sqrt{a}-1\right)\)

b: \(A=-a+\sqrt{a}-\dfrac{1}{4}+\dfrac{1}{4}=-\left(\sqrt{a}-\dfrac{1}{2}\right)^2+\dfrac{1}{4}< =\dfrac{1}{4}\)

Dấu '=' xảy ra khi a=1/4