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If x + y + z = 0, show that x^3 + y^3 + z^3 = 3xyz. - Mathematics

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

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Solution

We know that,

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

Now put (x + y + z) = 0,

xyz33xy(0)(x2 y2 z2 – x– y– xz)

⇒ x3 y3 z3 – 3xy0

⇒ x3 y3 z3 = 3xyz

Concept: Algebraic Identities
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APPEARS IN

NCERT Class 9 Maths
Chapter 2 Polynomials
Exercise 2.5 | Q 13 | Page 49

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