MathDB

infinitely many x,y such that sqrt (x+sqrt x) =y

Source: Romanian District Olympiad 2017, Grade X, Problem 1

October 10, 2018

Problem Statement

a) Determine

x\in\mathbb{N}

and

y\in\mathbb{Q}

such that

\sqrt{x+\sqrt{x}}=y.

b) Show that there are infinitely many pairs

(x,y)\in\mathbb{Q}^2

such that

\sqrt{x+\sqrt{x}} =y .