17

Part of 2018 Baltic Way

Problems(1)

A new variant of an old problem on rational approximations to square roots

Source: Baltic Way 2018, Problem 17

Prove that for any positive integers

p,q

\sqrt{11}>\frac{p}{q}

, the following inequality holds:

\sqrt{11}-\frac{p}{q}>\frac{1}{2pq}.