Question

Cho a + b + c = 0. Cm a³ + b³ + c³ = 3abc

Answer 1

Sao thì a + b + c cũng bằng 0

Answer 2

ta có: a3+b3+c3-3abc 

<=>a^3+3a^2b+3ab2+b3+c3-3a^2b-3ab^2-3abc

<=>(a+b)^3+c^3-3ab(a+b+c)

<=>(a+b+c)[(a+b)^2-c(a+b)+c^2.... tự làm bước tiếp

Answer 3

Ta sẽ chứng minh \(a^3+b^3+c^3-3abc=0\)

Ta có ; \(a^3+b^3+c^3-3abc=\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc\)

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

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

Vậy \(a^3+b^3+c^3=3abc\)

Answer 4

a3+b3+c3−3abc=(a+b)3+c3−3ab(a+b)−3abc=(a+b+c)(a2+b2+c2+2ab−ac−bc)−3ab(a+b+c)=(a+b+c)(a2+b2+c2−ab−bc−ac)=0Vậya3+b3+c3=3abc