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CBSE Class 9 Mathematics Question 28 of 30

Polynomials — Question 14

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14
Question

Question 14

Without actually calculating the cubes, find the value of each of the following:

(i) (-12)3 + (7)3 + (5)3

(ii) (28)3 + (-15)3 + (-13)3

Answer

(i) (-12)3 + (7)3 + (5)3

Here,

-12 + 7 + 5 = 0

As, x + y + z = 0

So, x3 + y3 + z3 = 3xyz

= 3 x (-12) x 7 x 5

= -1260

Hence, (-12)3 + (7)3 + (5)3 = -1260

(ii) (28)3 + (-15)3 + (-13)3

Here,

= 28 + (-15) + (-13)

= 28 - 15 - 13

= 0

As, x + y + z = 0

So, x3 + y3 + z3 = 3xyz

= 3 x 28 x (-15) x (-13)

= 16380

Hence, (28)3 + (-15)3 + (-13)3 = 16380