Assume $$𝑎$$ is a positive integer which is not a perfect square. Let $$𝑥, 𝑦$$ be non-negative integers such that $$\sqrt{x-\sqrt{x+a}} = \sqrt{a} - y$$. What is the largest possible value of $$𝑎$$ such that $$𝑎 < 100$$?

Video Solution