Would you please add a page explaining and demonstrating the uses of what I call related equations. A-level Maths has long included, towards the harder end of the course, exploring equations with related roots. E.g if an equation has roots p and q, what equation has roots 1/p and 1/q. I can see advantage in learning to manipulate algebra reliably so as to do this, but wondered what it was historically that prompted such work. I wondered whether the approach was indirect - I can't solve , but I can solve , so the original answer ought to look like ...? I expect part of the reply to come from differential equations, but is the non-maths bit that intrigues me - the maths, I can do that.