Question

[Big City Boy]

Cho a+b+c=0. CMR: \(a^3+b^3+c^3=3abc\)

Answer 1

[Bùi Thảo Vy]

a +b +c=0

⇔\(\left(a+b+c\right)^3\)

 ⇔\(a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^2+3a^2c+3ac^2+6abc=0\)

⇔\(a^3+b^3+c^3+\left(3a^2b+3ab^2+3abc\right)+\left(3b^2c+3bc^2+3abc\right)+\left(3a^2c+3ac^2+3abc\right)-3abc=0\)

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

Vì a+b+c= 0

⇒\(a^3+b^3+c^3=3abc\)

Chúc bạn học tốt!