SOLUTION: Prove the following inequality. Then state for which values the LHS equals the RHS. Please show and explain (in simple terms) every step in the solution. a^2 + b^2 >= 2 (a-b-

Algebra ->  Inequalities -> SOLUTION: Prove the following inequality. Then state for which values the LHS equals the RHS. Please show and explain (in simple terms) every step in the solution. a^2 + b^2 >= 2 (a-b-      Log On


   



Question 433306: Prove the following inequality. Then state for which values the LHS equals the RHS.
Please show and explain (in simple terms) every step in the solution.
a^2 + b^2 >= 2 (a-b-1)
Thank you.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I begin with a generally true statement, which is
%28a-1%29%5E2+%2B+%28b%2B1%29%5E2+%3E=+0
<==> a%5E2+-2a+%2B+1+%2B+b%5E2+%2B+2b+%2B+1+%3E=+0
<==> a%5E2+%2B+b%5E2+%3E=+2a+-+2b+-+2
<==> a%5E2+%2B+b%5E2+%3E=+2%28a+-+b+-+1%29.
Equality holds only if a = 1 and b = -1. (This is obvious if you look at the first inequality in this proof.)