I hope everyone has had a relaxing summer.
Anyway, I have ventured again into a realm of math that is far beyond my abilities, in other words I am trying to solve some mathematical problems from the book Challenging Mathematical Teasers by J.A.H. Hunter
The word problem I am currently solving leads to the following two equations
by substiuting we will have
This is about as far as I got, but then the solutions says something that I can't quite understand.
This equation is fully satisfied by: , and x= , where m is any rational number.
Could someone pleade exmplain the above thing to me? Does the author of this book use some systematic approach to solving these kind of equations with 3 unknowns or is it just the mathematician's creativity?
All responses are appreciated.