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

Asked by Furi 20th June 2016, 5:21 PM
Answered by 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 Expert 20th June 2016, 9:38 PM
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