# Homework Help: Proving an Inequality

1. Apr 4, 2012

### 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.

2. Apr 4, 2012

### 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

3. Apr 4, 2012

### babita

sry i typed the inequality wrong

4. Apr 4, 2012

### tms

The cases where $A = 0$ and $A = B$ should be obvious. For the rest, $0 < A < B$, think geometrically.