Question

Solve the following equations:
$2\sqrt{x}+2x^{-\frac{1}{2}}=5$.

Answer 1

$2\sqrt{x}+2x^{-\frac{1}{2}}=52\sqrt{x}+\frac{2}{\sqrt{x}}=5$

Put $\sqrt{x}=t$

$2t+\frac{2}{t}=52t^2+2=5t2t^2-5t+2=02t^2-4t-t+2=02t(t-2)-1(t-2)=0(2t-1)(t-2)=0t=\frac{1}{2},2\sqrt{x}=t\Rightarrow x=t^{2}x={\left(\frac{1}{2}\right)}^2,2^{2}x=\frac{1}{4},4$