Question

Cho a+b+c+d=0. Chứng minh rằng: a³+b³+c³+d³=3(c+d)(ab-cd).

Answer 1

a+b+c+d=0

=>c+d=-a-b

\(a^3+b^3+c^3+d^3\)

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

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

\(=3ab\left(c+d\right)-3cd\left(c+d\right)\)

=3(c+d)(ab-cd)