Prove that x<y
Source: Turkey JBMO Team Selection Test 2013, P5
May 31, 2013
inequalities proposedinequalities
Problem Statement
Let be real numbers greater than and be real numbers such that a^x+b^y = (a^2+b^2)^x \text{and} c^x+d^y = 2^y(cd)^{y/2}
Prove that .