If X3 +Y3 + Z3 =3XYZ and X+Y+Z =0 find the value of :- (X+Y)2/XY + ( Y +Z )2/YZ + (Z+X)2 / Z
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Solution : We know that x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx). If x + y + z = 0, then x3 + y3 + z3 – 3xyz = 0 or x3 + y3 + z3 = 3xyz.
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