Register to reply

Proving an Inequality

by ausdreamer
Tags: inequality, proving
Share this thread:
Apr4-12, 06:22 PM
P: 23
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


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.
Phys.Org News Partner Science news on
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Apr4-12, 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
Apr4-12, 06:29 PM
P: 61
sry i typed the inequality wrong

Apr4-12, 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.

Register to reply

Related Discussions
Proving an inequality Calculus & Beyond Homework 6
Proving an inequality Calculus & Beyond Homework 3
Proving inequality Calculus 2
Help proving an inequality Calculus & Beyond Homework 15
Proving an Inequality Introductory Physics Homework 6