If $x (5-\frac{2}{x})=\frac{5}{x}$, then the value of $x^2 +\frac{1}{x^2}$ is equal to :

$2\frac{4}{25}$

If $x (5-\frac{2}{x})=\frac{5}{x}$,

then,

5x - \(\frac{5}{x}\) = 2

Squaring on both the sides,

25x² + \(\frac{25}{x^2}\) = 4 + 2×25

= 25x² + \(\frac{25}{x^2}\) = 54

Divide the equation by 25 on the both sides,

then the value of $x^2 +\frac{1}{x^2}$ = \(\frac{54}{25}\) = $2\frac{4}{25}$