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Surds

I need hep in 87 step 2 q3

Thing is, I don't even know where to start.

Can anyone give hints as to how I should do this question.

Thanks

Well, there are a couple of things I think when I look at it.

A first step might be to try to understand the expressions defining M+s and N-r. Can you expand the brackets? That won't necessarily help you to do the question, but if you've not tried anything it's something you know to try if you're stuck.

If that's no use, think about *why* the restriction on the values of b matters. In general, it will certainly be possible for M to be nonzero, so it must be something about these special values of b that forces M to be 0. Can you take the inequality b < 2a-1 and use it to come up with an inequality relevant to the value of M?

In general, when you're stuck on where to start with a question, it's a good idea to collect all of the information that you know, and see what you can apply to that information (be it expanding brackets, applying theorems, sketching curves) even if you're not sure where you'll end up - you might learn something.

I guess it's because if I let b=2a-1 then the quadratic turns into (a-1)^2. Square rooting that you get (a-a+1)^n, which turns out to be 1. So I end up with the equation 1=M+s. But how can I use this to show that M=0. Am I even on the right track?

You have an equation, which shows what would happen if b=2a-1. Can you express an inequality as we know b is strictly less than 2a-1?

Also, obligatory reminder that STEP has changed a lot since 1987, so we do advise spending time on recent questions before digging too far back in the archives...

This question is too hard can someone tell me how to do the answer

This is quite a hard question, and is also almost 30 years old! I would suggest trying 2004 S1 Q1 and 2004 S2 Q1 first. Then have another look at this one.