MathDB

5

Part of 2013 JBMO TST - Turkey

Problems(1)

Prove that x<y

Source: Turkey JBMO Team Selection Test 2013, P5

5/31/2013
Let a,b,c,da, b, c ,d be real numbers greater than 11 and x,yx, y 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 x<yx<y.
inequalities proposedinequalities