SOLUTION: Prove that if a>b>0 then a^3>b^3

Algebra ->  Proofs -> SOLUTION: Prove that if a>b>0 then a^3>b^3      Log On


   



Question 1005817: Prove that if a>b>0 then a^3>b^3
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E3%22%22%3E%22%22b%5E3

a%5E3-b%5E3%22%22%3E%22%220

%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%22%22%3E%22%220

The products and sums of positive 
number are positive, therefore

Since a > b then a-b > 0

Since a > 0 and b > 0 then a2 > 0, b2 > 0, and ab > 0.

%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29 is positive or

%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%22%22%3E%22%220

Edwin