(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

#1 If |x -2| < p, where x < 2, then x - p =

i have obtained an inequality at most.

#2 For what value of the coefficient a do the equations x^{2}-ax + 1 = 0 and x^{2}- x + a = 0.

#3 Let R be a rectangle. How many circles in the plane of R have a diameter both of whose endpoits are vertices of R?

3. The attempt at a solution

#1 -p < x-2 < p

eventually i obtain:

-2p + 2 < x - p < 2

#2 I have tried solving simultaneously but i have obtained and equation with both a and x.

i have also tried equating coefficients but i obtain a = 1. The actual answer is -2.

#3 is that 6? because there are 6 different ways of joining 2 vertices in the rectangle.

thnks

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# Homework Help: Maths competition problems

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