Question

Cho a+b+c=0.CM
a^3+b^3+c^3=3abc
Mong cb giúp đỡ mình ^_^

Answer 1

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

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

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

mà a+b= -c (cmt )

nên \(a^3+b^3+c^3=3abc\left(đpcm\right)\)

Answer 2

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

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

\(=-3a^2b-3ab^2=3ab\left(-a-b\right)=3abc\) (đpcm)

Answer 3

a+b+c=0 =>(a+b+c)^3=0

=>a^3+b^3+c^3+(3a^2b+3ab^2+3abc)+(3b^2c+3bc^2+3abc)+(3c^2a+3a^2c+3abc)-3abc=0

=>a^3+b^3+c^3+3ab(a+b+c)+3bc(a+b+c)+3ac(a+b+c)-3abc=0

=>a^3+b^3+c^3=3abc