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# Is this proof valid? (1)

I have a book, which states this inequality and need to be proof. Absolutely, this is a problem.

Given $$a,b \in \mathbb{R}^+$$ and $$a\neq b$$, proof that $a^{3} +b^{3} > a^{2}b +ab^{2}$

Proof: since $$a \neq b$$, obviously that $a+b>0$ $(a-b)^2>0$

Multiply both ineqs and we have $(a+b)(a-b)^2>0$ $(a+b)(a^2-2ab+b^2)>0$ $a^3-a^2b-ab^2+b^3>0$ $a^3+b^3>a^2b + ab^2$

Done!

Is that valid? Comments will be appreciated!

Note by Figel Ilham
1 year, 10 months ago