Cubic Convenience FactorDate: 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/ |
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