Question

 

 

Answer 1

2: \(a^3+b^3>=ab\left(a+b\right)\)

=>\(\left(a+b\right)\left(a^2-ab+b^2\right)-ab\left(a+b\right)>=0\)

=>\(\left(a+b\right)\cdot\left(a^2-ab+b^2-ab\right)>=0\)

=>\(\left(a+b\right)\left(a-b\right)^2>=0\)

Vì a>0 và b>0 nên a+b>0

mà \(\left(a-b\right)^2>=0\forall a,b>0\)

nên \(\left(a+b\right)\left(a-b\right)^2>=0\forall a,b>0\)

=>\(a^3+b^3>=ab\left(a+b\right)\)(ĐPCM)