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Class 10 > If x + y + z = 0, show that: (cube of x) + (cube of...
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If x + y + z = 0, show that: (cube of x) + (cube of y) + (cube of z) = 3xyz?

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We know that, a 3 + b 3 + c 3=(a + b + c)(a 2 + b 2 + c 2 - ab - bc - ca) + 3abc. Substitute (a + b +c) = 0 in above equation: => a 3 + b 3 + c 3=0 x (a 2 + b 2 + c 2 - ab - bc - ca) + 3abc=>a 3 + b 3 + c 3 = 3abc.
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