Without actually calculating the cubes, find the value of the following:- (28)^3 + (–15)^3 + (–13)^3 - Mathematics

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Without actually calculating the cubes, find the value of the following:- (28)3 + (–15)3 + (–13)3

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Solution

(28)3 + (–15)3 + (–13)3 

Let x = 28, y = −15, and z = −13

It can be observed that,

x + y + z = 28 + (−15) + (−13) = 28 − 28 = 0

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

x3 + y3 + z3 = 3xyz

∴ (28)3 + (–15)3 + (–13)3 = 3(28)(-15)(-13) = 16380

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Chapter 2: Polynomials - Exercise 2.5 [Page 49]

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NCERT Mathematics Class 9
Chapter 2 Polynomials
Exercise 2.5 | Q 14.2 | Page 49

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