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Proving an Inequality 
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#1
Apr412, 06:22 PM

P: 23

1. The problem statement, all variables and given/known data
If 0 <= A <= B, prove that: A(BA) <= (B/2)^2 2. Relevant equations  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
Apr412, 06:28 PM

P: 61

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
Apr412, 06:29 PM

P: 61

sry i typed the inequality wrong



#4
Apr412, 06:50 PM

P: 616

Proving an Inequality
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.



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