Question

giup mik voi

Answer 1

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

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

b: |Q|>-Q

=>|Q|+Q>0

=>Q>0

=>\(\dfrac{2}{x-1}>0\)

=>x-1>0

=>x>1

c: Để Q nguyên thì \(2⋮x-1\)

=>\(x-1\in\left\{1;-1;2;-2\right\}\)

=>\(x\in\left\{2;0;3;-1\right\}\)

mà x>0 và x<>1

nên \(x\in\left\{2;3\right\}\)