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Without actually calculating the cubes, find the value of the following:- (–12)^3 + (7)^3 + (5)^3 - Mathematics

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Without actually calculating the cubes, find the value of the following:- (–12)3 + (7)3 + (5)3 

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Solution

(–12)3 + (7)3 + (5)3

Let x = −12, y = 7, and z = 5

It can be observed that,

x + y + z = − 12 + 7 + 5 = 0

It is known that if x + y + z = 0, then

x3 + y3 + z3 = 3xyz

∴ (–12)3 + (7)3 + (5)3 = 3(-12)(7)(5) = -1260

Concept: Algebraic Identities
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APPEARS IN

NCERT Class 9 Maths
Chapter 2 Polynomials
Exercise 2.5 | Q 14.1 | Page 49

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