SOLUTION: If the lengths of the sides of a right triangle are, in increasing order, a, b, and c. Prove that a^3+b^3<c^3 ( a cube plus b cube is less than c cube)

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Question 475152: If the lengths of the sides of a right triangle are, in increasing order, a, b, and c. Prove that a^3+b^3
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The inequality is true iff







The a^6 + b^6 on both side cancel out, so we want to show for positive a,b



Divide both sides by (a^2)(b^2)



By AM-GM inequality,

This implies that , so we're done.