Question

Cho a + b+ c =0 Cm \(a^3+b^3+c^3=3abc\)

Answer 1

Ta có: \(VT=a^3+b^3+c^3\)

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

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

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

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

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

\(=3abc=VP\) ( do a + b + c = 0 )

\(\Rightarrowđpcm\)