If x+y+z=0 , then show that x cube +y cube + Z cube = 3XYZ

Asked by Furi | 20th Jun, 2016, 05:21: PM

Expert Answer:

begin mathsize 16px style Recall space the space identity comma
straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz equals left parenthesis straight x plus straight y plus straight z right parenthesis left parenthesis straight x squared plus straight y squared plus straight z squared minus xy minus yz minus xz right parenthesis
So space if space straight x space plus space straight y plus space straight z space equals space 0 space then comma
rightwards double arrow straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz equals left parenthesis 0 right parenthesis left parenthesis straight x squared plus straight y squared plus straight z squared minus xy minus yz minus xz right parenthesis
rightwards double arrow straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz equals 0
rightwards double arrow straight x cubed plus straight y cubed plus straight z cubed equals 3 xyz end style

Answered by Rebecca Fernandes | 20th Jun, 2016, 09:38: PM