Question 55
The real numbers $a$ and $b$ fulfill the conditions $a, b \ge 0$ and $2a\sqrt{b+1} + 2b\sqrt{a+1} = (\sqrt{a} + \sqrt{b})(a+b+1)$. Prove that $a+b=1$.
MathNet 2017-part-05 — 176 problems (EN–VI) Question 55
Math Olympiad Vault · MathNet 2017-part-05 — 176 problems (EN–VI)