Question

Without any actually calculating the cube, find the value of (1/2)cube +(1/3)cube - (5/6) cube

Answer 1

If a+b+c = 0 , then (a)cube + (b)cube + (c)cube = 3abc

1/2 + 1/3 - 5/6

= 5/6 - 5/6

= 0

Therefore , 3(1/2)(1/3)(5/6)

= 5/12