# KS5 nrich question on &quot;dodgy proofs&quot;

Discussion in 'Mathematics' started by stevencarrwork, Nov 1, 2011.

1. ### stevencarrwork

I noticed that EDEXCEL FP2 solve a lot of inequalities by doing things like multiplying by (x+1)^2(x-2)^2.

Is this entirely valid, as if 3 > 1, then it is not true that 3 times 0 > 1 times 0?

What happens if you multiply by (x+1)^2 and x = -1?

But the book just does that sort of multiply all the time.

2. ### stevehewson

I lik D Franklin's explanation.

3. ### D Franklin

It's valid with the proviso that "you need to pay attention at the points where you're multiplying by 0".

Typically you'd multiply by (x+1)^2 where there's a division by (x+1) somewhere in the original expression. In which case x = - 1 is not going to be a valid solution point. In most cases, this will happen "automatically" when you multiply by (x+1)^2, but if I was actually doing a question I wouldn't rely on it. It only takes a couple of moments to 'sanity check' the end points. On the other hand, I don't think you need to explicitly say that you've done the sanity check.

For what it's worth, this is the approach Siklos advocates for inequalities in the STEP guides, so that's a validation from someone reasonably well qualified.