Whats the value?

Algebra Level 2

if x = 42, y = 37, z = -79, find the value of x 3 + y 3 + z 3 3 x y z x^{3} + y^{3} + z^{3} - 3xyz

0 1300 4520 1

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2 solutions

Genis Dude
Aug 30, 2017

x 3 + y 3 + z 3 3 x y z = ( x + y + z ) ( x 2 + y 2 + z 2 x y y z z x ) x^3+y^3+z^3 -3xyz= (x+y+z)(x^2+y^2+z^2-xy-yz-zx)

A s , As, x + y + z = 0 , x+y+z=0,

x 3 + y 3 + z 3 3 x y z = 0 x^3+y^3+z^3 -3xyz=0

Atvthe King
Jul 9, 2020

Taking the equation modulo 3 yields that 0 is the only possible answer.

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