if x+y+z=0, then show that x3+y3+z3=3xyz, how can we solve this math problem. if x+y+z=0, then show that x3+y3+z3=3xyz, i need to prove if x+y+z=0, x3+y3+z3=3xyz.
if x+y+z=0, then show that x3+y3+z3=3xyz
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if x+y+z=0, then show that x3+y3+z3=3xyz, how can we solve this math problem. if x+y+z=0, then show that x3+y3+z3=3xyz, i need to prove if x+y+z=0, x3+y3+z3=3xyz.
Ridhi Mehta
The question is x+y+z=0 then show that x³+y³+z³=3xyz? Solving this problem is easy and I’ll explain you clearly with step by step simple explanation.
Given:x+y+z=0—¹
To show:x³+y³+z³=3xyz
Solution Take equation 1
x+y+z=0
x+y=-z—a
Cubing both sides
{Using identity (a+b)³=a³+b³+3a²b+3ab²}
(x+y)³=(-z)³
x³+y³+3x²y+3xy²=-z³
Taking 3xy common
x³+y³+3xy(x+y)=-z³
Replacing (x+y) by -z using a
x³+y³-3xyz=-z³
Taking -z³ left side and -3xyz on right side
x³+y³+z³=3xyz
Hence proved.
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