Question

Chung minh dang thuc sau:

a​3-b​​3+ab(a-b)=(a-b)(a+b)²

Answer 1

Trieu Trong Thai

 CM a3+b3+c2 >= ab+bc+ac (*) 
2a^2 +2b^2 +2c^2 - 2ab -2bc -2ac = (a-b)^2 + (b-c)^2 + (a-c)^2 >= 0 

từ * => a^2 +b^2+c^2 +2ab+2bc+2ac >= 3ab+3bc+3ac <=> (a+b+c)^2 >= 3ab +3ac+3bc 
từ * => 2ab +2ac+2bc+ a^2+b^2+c^2 =< 3a^2+3b^2+3c^2 <=> (a+b+c)^2 =< ... 

Answer 2

de bai sai sua lai la

\(a^3-b^3+ab\left(b-a\right)=\left(a-b\right)\left(a+b\right)^2\)

bien doi ve phai ta co:

\(\left(a-b\right)\left(a+b\right)^2\)

\(=a^3+ab^2-a^2b-b^3\)

\(=a^3-b^3+ab\left(b-a\right)\)= ve trai

vay \(a^3-b^3+ab\left(b-a\right)=\left(a-b\right)\left(a+b\right)^2\)