on page 426 of introducing pure mathematics, qu 10 has 2 parts. Am I supposed to answer part b with reference to part a? I can do it the long winded way but that word DEDUCE in part b has me thinking. Help
Hi I,m on holiday at the moment but will be back on saturday. I had a go at nearly all the questions in the book and have kept the answers. I'll get back to you ASAP. I did my a levels in 1969 and visited that book about 5 yrs ago. It's great isn't it.
OK I'm home now and have the solution. You have proved part a I believe. You will have found therefore that (ax + b)/(cx +d) = (b-xd)/(cx-a). At this point, cross multiply and gather like terms and faactorise. You end up with x^2c(a+d) - x(a^2 - d^2) - b(a + d) = 0. (x^2 means x squared). Now use the quadratic formula to find the roots of that equation. It will rely on you spotting the use of the difference of 2 squares i.e. (a^2 - d^2) = (a +d) (a-d). The term under the sqare root sign can evenually be simplufied to (a+d)^2[(a-d)^2 + 4bc]. From the question, this evaluates to zero hence there is only one root therefore only one point of intersection.
I hope that this has helped. If you are still stuck I will e-mail you a copy of the solution.
Thank you for posting your comment, it has made me smile.