NIMCET 2021 — Mathematics PYQ

Let $a$ and $b$ be the sides of triangle
$a+b=x\Rightarrow ab=y$
Given, $x^2-z^2=y$
Here, $z$ is its third side.

$$\begin{array}{rl}& amp;(a+b{)}^2-z^2=ab\Rightarrow a^2+b^2+2ab-z^2=ab\\ & amp;a^2+b^2+ab=z^2\Rightarrow a^2+b^2-z^2=-ab\\ & amp;\frac{a^2+b^2-z^2}{2ab}=-\frac{1}{2}\Rightarrow \cos C=\frac{2\pi }{3}\end{array}$$