Question

Answer 1

a)

Với `a>2`

\(=-\left(a-2\right)\sqrt{\dfrac{2a}{a-2}}\\ =-\sqrt{\dfrac{2a\left(a-2\right)^2}{a-2}}\\ =-\sqrt{\dfrac{2a\left(a-2\right)^2}{a-2}}\\ =-\sqrt{2a\left(a-2\right)}\\ =-\sqrt{2a^2-4}\) 

b)

Với `0<x<5`:

\(=-\left(5-x\right)\sqrt{\dfrac{x}{\left(5-x\right)\left(5+x\right)}}\\ =-\sqrt{\dfrac{x\left(5-x\right)}{\left(5-x\right)\left(5+x\right)}}\\ =-\sqrt{\dfrac{x}{5+x}}\\ =-\dfrac{\sqrt{x}}{\sqrt{5+x}}\)

c)

Với `0<a<b`:

\(=-\left(b-a\right)\sqrt{\dfrac{3a}{\left(b-a\right)\left(b+a\right)}}\\ =-\sqrt{\dfrac{3a\left(b-a\right)}{\left(b-a\right)\left(b+a\right)}}\\ =\dfrac{\sqrt{3a}}{\sqrt{b+a}}\)