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a -\sqrt{ab}, b+ \sqrt{ab} rationals 2012 Romania District VIII p1

Source:

September 1, 2024

algebrarational

Problem Statement

Let

a

and

b

be distinct positive real numbers, such that

a -\sqrt{ab}

and

b -\sqrt{ab}

are both rational numbers. Prove that

a

and

b

are rational numbers.