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,


x3 + y3 + z3 = 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,


x3 + y3 + z3 = 3xyz


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


= 16380


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