Problem

Source: Indonesian National Mathematical Olympiad 2024 Problem 1

Tags: algebra, Manipulation, system of equations, Indonesia, Inamo, Indonesia MO



Determine all positive real solutions $(a,b)$ to the following system of equations. \begin{align*} \sqrt{a} + \sqrt{b} &= 6 \\ \sqrt{a-5} + \sqrt{b-5} &= 4 \end{align*}