Question

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 1

(i) (–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

(ii) (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