SOLUTION: If 2x=a+b+c, show that (x-a)^2 + (x+b)^2 + (x-c)^2 +x^2 = a^2 + b^2 + c^2.

Algebra ->  Equations -> SOLUTION: If 2x=a+b+c, show that (x-a)^2 + (x+b)^2 + (x-c)^2 +x^2 = a^2 + b^2 + c^2.      Log On


   

Question 1109037: If 2x=a+b+c, show that (x-a)^2 + (x+b)^2 + (x-c)^2 +x^2 = a^2 + b^2 + c^2.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
   (x-a)^2 + (x+b)^2 + (x-c)^2 +x^2  =  (open parentheses) = 

=  (collect like terms linear in  "x" ) = 

= (next use the given identity) = a^2 + b^2 + c^2.

QED.