Analytical solution to $\sqrt{a^2-x^2} + \sqrt{b^2-x^2} = \sqrt{a^2-x^2} \cdot \sqrt{b^2-x^2}$ Can't find beauty analytical solution to such equation :
$$\sqrt{a^2-x^2} + \sqrt{b^2-x^2} = \sqrt{a^2-x^2}\cdot\sqrt{b^2-x^2}$$
Assuming $a,\ b \in \mathbb{N},\ a \le b,\ x \in \mathbb{R}$
Is it possible to find a solution for general case?

So, we have $$\dfrac1{\sqrt{a^2-x^2}}+\dfrac1{\sqrt{b^2-x^2}}=1$$
WLOG $a^2-x^2=\sin^4t, b^2-x^2=\cos^4t$
$\implies b^2-a^2=\cos2t$
$$4a^2-4x^2=(2\sin^2t)^2=(1+a^2-b^2)^2$$
$$\iff4x^2=?$$
