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KS5 nrich question on "dodgy proofs"

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

  1. 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. I lik D Franklin's explanation.
  3. 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.

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