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If x+y+z = 0, show that x3+y3+z3 = 3xyz. Q.13

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Please give me the best way for solving the problem of class 9th ncert math of Polynomials chapter of math of class 9th of exercise 2.5 of question no  13  what is the tricky way for solving this question

If x+y+z = 0, show that x3+y3+z3 = 3xyz.


1 Answer

  1. We know that,

    x3+y3+z3-3xyz = (x +y+z)(x2+y2+z2–xy–yz–xz)

    Now, according to the question, let (x+y+z) = 0,

    then, x3+y3+z3 -3xyz = (0)(x2+y2+z2–xy–yz–xz)

    ⇒ x3+y3+z3–3xyz = 0

    ⇒ x3+y3+z3 = 3xyz

    Hence Proved

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