Question

cho a+b+c=0.Chứng minh a³+b³+c³=3abc

Answer 1

Ta có: \(a+b+c=0\Rightarrow a+b=-c\Rightarrow\left(a+b\right)^3=\left(-c\right)^3\)

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

\(\Rightarrow a^3+b^3+c^3+3ab.\left(-c\right)=0\Rightarrow a^3+b^3+c^3-3abc=0\)

\(\Rightarrow a^3+b^3+c^3=3abc\) => đpcm

Answer 2

Ta có VT=a³+b³+c³

=(a+b)(a²-ab+b²)+c

= -c(a²-ab+b²)+c³

= -c [(a+b)²-3ab-c²]

= -c[ c²-3ab-c²]

= 3abc=VP (đpcm)

Chúc bạn may mắn!