Q. 144.3( 185 Votes )

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

(i)

(ii)

Answer :

(i) Let x = -12, y = 7 and z = 5

We observed that,

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

We know that if,

x + y + z = 0

Then,

x^{3} + y^{3} + z^{3} = 3xyz

(-12)^{3} + (7)^{3} + (5)^{3} = 3 (-12) (7) (5)

= -1260

(ii) Let x = 28, y = -15 and z = -13

We observed that,

x + y + z = 28 – 15 – 13 = 0

We know that if,

x + y + z = 0

Then,

x^{3} + y^{3} + z^{3} = 3xyz

(28)^{3} + (-15)^{3} + (-13)^{3} = 3 (28) (-15) (-13)

= 16380

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