Question

Cho biểu thức :

P = [(√x - 2/ x-1)- (√x+2 /x+2√x+1)×(1-x/√2)²

^{a) rút gọn biểu thức P}

^{b) cm: nếu 0<x<1 thì P >0}

^{c) tìm GTLN của P}

^{giúp t bài này vs!!! Tks nhìu!~}

Answer 1

\(_{_0_00_00_00_00_000_{ }0_00_00_00_00_00_00_00^{00}0^00^00^00^00^00^00^00^00^00^00_00_00_00_00_00_00_00_00_00_00_00_00_0}\)

Answer 2

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

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

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

b: Để P>0 thì \(\sqrt{x}\left(\sqrt{x}-1\right)< 0\)

=>căn x-1<0

=>0<x<1