If #a+b+c=6#, find the value of #(2-a)^3+(2-b)^3+(2-c)^3- 3(2-a)(2-b)(2-c)#?

1 Answer
Ratnaker Mehta
Apr 14, 2018

# 0#.

Explanation:

Recall that, #x+y+z=0 iff x^3+y^3+z^3=3xyz......(diamond)#.

Set, #x=2-a, y=2-b, and, z=2-c#.

Then, #x+y+z=(2+2+2)-(a+b+c)#

#=0......."[because, a+b+c=6, Given]"#.

#:. x^3+y^3+z^3=3xyz......[because, (diamond)]#.

# rArr" The Reqd. Value"=0#.

Related questions
Impact of this question
13451 views around the world
You can reuse this answer
Creative Commons License