Question

14. Without actually calculating the cubes, find the value of each of the following:
(i) (-12)3 + (7)3 + (5)3
(ü) (28) +(-15)3 +(-13)3
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Answer 1

Step-by-step explanation:

1. refer to the attachment for better understanding

Answer 2

Answer:

(-12)³ + (7)³+ (5)³

Let x = -12, y =7&z=5

x + y + z = -12 + 7 + 5 = 0

Here, x + y + z = 0

We know that if,

x + y + z = 0, then x³ + y³ + z³ = 3xyz (-12)³ + (7)³ + (5)³ = 3(-12)(7)(5) = -1260

(-12) ³+ (7)³+ (5)³ = - 1260

(ii) (28)3 + (-15)³ + (-13)³

Let x = 28, y = -15 and z = -13

x + y + z = 28-15-13 = 0

Here, x + y + z = 0

We know that if, x + y + z = 0,

then x³ + y² + z³ = 3xyz

(28)3³+ (-15)3 + (-13)³ = 3(28)(-15)(-13)

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