Question

[dinh khanh toan]

cho x+y+z=0 CMR x^3+y^3+z^3=3x*y*z

Answer 1

[Phạm Tuấn Đạt]

Xét \(x^3+y^3+z^3-3xyz\)

\(=\left(x+y\right)^3-3x^2y-3xy^2+z^3-3xyz\)

\(=\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy.0\)

\(=0-0=0\)

Vậy \(x^3+y^3+z^3=3xyz\)