Question

Cho \(a+b+c=0\)

CM \(a^3+b^3+c\left(a^2+b^2\right)=abc\)

Giúp mk với, sắp đi học r!!

Answer 1

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

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

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

\(=abc\)

Answer 2

\(a+b+c=0\Rightarrow c=-a-b\)

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

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

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

\(=ab\left(-a-b\right)\)

\(=abc\) (ĐPCM)

tick cho cáilàm mệt lắm mới ra