Question

[CR7]

cho a+b+c=0.chung minh rang:a^3+b^3+c^3=3abc

Answer 1

[Nhok Ngôk Nghêk]

a+b+c =0 => b+c=-a => (b+c)^3=-a^3 

Answer 2

[Phước Nguyễn]

Do \(a+b+c=0\Rightarrow a+b=-c\)

Ta có hằng đẳng thức: \(\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\)

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

Do đó: \(a^3+b^3+c^3=\left(a+b\right)^3+c^3-3ab\left(a+b\right)=\left(-c\right)^3+c^3-3ab.\left(-c\right)=3abc\left(đpcm\right)\)