Question

Cho a + b + c = 0. Chứng minh rằng : a³ + a²c - abc + b²c + b³ = 0

Answer 1

Ta có :

\(a^3+a^2c-abc+b^2c+b^3=0\)

\(\Leftrightarrow\left(a^3+b^3\right)+\left(a^2c-abc+b^2c\right)=0\)

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

\(\Leftrightarrow\left(a^2-ab+b^2\right)\left(a+b+c\right)=0\) ( Luôn đúng vì \(a+b+c=0\) )

Wish you study well !!