if X + Y + Z=0 then verify that x3+y3+z3=0
MonsieurBrainly:
x3+y3+z3 will be 3xyz and not 0
write a solution
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h bil kul
3 (n)+3 (n)+3 (n)=0 so n=0 then
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x3 + y3 + z3 3xyz = (x + y + z) (x2 + y2 + z2 xy yz zx) Putting x + y + z = 0, x3 + y3 + z3 3xyz = (0) (x2 + y2 + z2 xy yz zx) x3 + y3 + z3 3xyz = 0 x3 + y3 + z3 = 3xyz Hence proved.
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Given, x3 + y3 + z3 = 3xyz
Therefore, x3 + y3 + z3 - 3xyz =0
This means,
x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
Now if x + y + z = 0, then......
x3 + y3 + z3 - 3xyz = ( 0 ) (x2 + y2 + z2 - xy - yz - zx) . . . . . . .... ..... ... .. . . .. . ..... [ subsituting the value of x + y + z ]
x3 + y3 + z3 - 3xyz = 0
x3 + y3 + z3 = 3xyz .
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