Question

at%20%5C%3A%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%20%20%7By%7D%5E%7B3%20%7D%20%20%2B%20%20%7Bz%7D%5E%7B3%7D%20%20%3D%203xyz" id="TexFormula1" title="if \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} = 3xyz" alt="if \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} = 3xyz" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

Given

x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3 +y 3 +3x 2y+3xy 2 =−z 3

⟹x 3 +y 3 +3xy(x+y)=−z 3

⟹x 3+y 3+3xy(−z)=−z 3

⟹x 3 +y 3−3xyz=−z 3

⟹x 3 +y 3 +z 3 =3xyz

Step-by-step explanation:

Hope it is helpful.....