olymmath

BALTIC-WAY 2002 Problem 5

  • Answer

Find all pairs (a,b)(a, b) of positive rational numbers such that

a+b=2+3.\sqrt{a}+\sqrt{b}=\sqrt{2+\sqrt{3}} .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(a, b)=\left(\frac{1}{2}, \frac{3}{2}\right) \text{ or } (a, b)=\left(\frac{3}{2}, \frac{1}{2}\right)

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Locator baltic-way/2002/p5 · Tag A872RDZXPD · Edit this page on GitHub · Keys: j next, k previous