How Does Proof by Contradiction Validate a/b + b/a >= 2?

[chan8366]

[SOLVED] basic math proof by contradiction

Homework Statement

prove: If a and b are positive numbers, a/b +b/a>=2

Homework Equations

The Attempt at a Solution

by contradiction (a^2+b^2)/ab<2 and got lost

 

[Dick]

If (a^2+b^2)/ab<2 then a^2+b^2<2ab. So a^2+b^2-2ab<0. But a^2+b^2-2ab=(a-b)^2<0. What could be wrong with that?

 

[chan8366]

thanks it was that easy