Cubic Convenience Factor

Date: 11/15/2010 at 02:56:18
From: Rahul
Subject: if a+b+c=7,then find  the value of (a-2)^3+(b-4)^3+(c-1)^3 ?

I cannot solve this question: if ...

   a + b + c = 7,
   
... then find the value of

   (a - 2)^3 + (b - 4)^3 + (c - 1)^3

Date: 11/15/2010 at 07:57:58
From: Doctor Ali
Subject: Re: if a+b+c=7,then find  the value of (a-2)^3+(b-4)^3+(c-1)^3 ?

Hi Rahul!

Thanks for writing to Dr. Math.

This problem can be solved by one of the results that we get from the
following identity:

   x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - xz - yz)

Please check whether you can find it out yourself or not. Just note that
if you consider ...

   x = a - 2
   y = b - 4
   z = c - 1

... then according to what your problem gives you, we can get that

   x + y + z = 0

So,

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

Does that make sense?

Please write back if you still have any difficulties.

- Doctor Ali, The Math Forum
  http://mathforum.org/dr.math/