Nonadjacent Integer Radicals

★ 7/10number theory Monotonicity algebra Estimation

Problem

Let $x, y \ge 0$ , and set

a = \sqrt{x} + \sqrt{y}, \qquad b = \sqrt{x+2} + \sqrt{y+2}.

Given that $a$ and $b$ are integers that are not consecutive, find $a$ and $b$ .

Answer

Solution

Difficulty	7/10
Topics	number theory, Monotonicity, algebra, Estimation

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