Proving an Inequality

ausdreamer

1. The problem statement, all variables and given/known data

If 0 <= A <= B, prove that: A(B-A) <= (B/2)^2

2. Relevant equations

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3. The attempt at a solution

I've been blindly rearranging the terms trying to see a way to prove this but due to my complete lack of experience in proofs, I'm hoping someone here can give a little push in a helpful direction.

babita

try opening the brackets and taking all the terms to one side. it'll become square of a number.
but i dnt understand how 0>=a>=b are essential conditions for this. square of any real no would always be positive

babita

sry i typed the inequality wrong

tms

The cases where [itex]A = 0[/itex] and [itex] A = B[/itex] should be obvious. For the rest, [itex]0 < A < B[/itex], think geometrically.