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) (Show Source): You can put this solution on YOUR website!
The inequality is true iff
^2 < (c^3)^2 = c^6)
^2 < (a^2 + b^2)^3)
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.
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