Question

Cho biểu thức P = \(\dfrac{\sqrt{a}\left(1-a\right)^2}{1+a}:\left(\left(\dfrac{1-\sqrt{a^3}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1+\sqrt{a^3}}{1+\sqrt{a}}-\sqrt{a}\right)\right)\)

a) Rút gọn P.

b) Xét dấu của biểu thức M = \(a\left(P-0,5\right)\)

Answer 1

a: \(P=\dfrac{\sqrt{a}\left(1-a\right)^2}{1+a}:\left[\left(a+2\sqrt{a}+1\right)\left(a-2\sqrt{a}+1\right)\right]\)

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

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

\(\Leftrightarrow a\left(P-\dfrac{1}{2}\right)< 0\)