solve for x the equation :
$\displaystyle x+ \sqrt{a^2+x^2} = \frac{5a^2}{ a^2+b^2}$
Take x from both sides and square:
$\displaystyle a^2+x^2 = (\frac{5a^2}{ a^2+b^2} - x)^2 = \frac{25a^4}{(a^2+b^2)^2} - \frac{10a^2x}{a^2+b^2} + x^2$
$\displaystyle x^2$ will cancel. Rearranging gives:
$\displaystyle \frac{10a^2}{a^2+b^2}x = \frac{25a^4}{(a^2+b^2)^2}$
From there solve for x
here is a mistake it is not $\displaystyle b$ but $\displaystyle x$, sorry.
the right equation: $\displaystyle x+ \sqrt{a^2+x^2} = \frac{5a^2}{ a^2+x^2}$
i have a question for e^(i*pi) : did you forget $\displaystyle a^2$ here : $\displaystyle \frac{10a^2}{a^2+b^2}x = \frac{25a^4}{(a^2+b^2)^2}
$ or am i wrong?