- #1
ArcanaNoir
- 779
- 4
Homework Statement
I'm trying to show that [itex] f(x,y)=x\sqrt{1+y^2}+y\sqrt{1+x^2} [/itex] is associative, or provide a counter example. (All variables are real numbers.)
Homework Equations
The Attempt at a Solution
I have it down to needing to show that [tex] x\sqrt{(1+y^2)(1+z^2)}+z\sqrt{1+(x\sqrt{1+y^2}+y\sqrt{1+x^2})^2} [/tex] is equal to [tex] z\sqrt{(1+x^2)(1+y^2)}+x\sqrt{1+(z\sqrt{1+y^2}+y\sqrt{1+z^2})^2} [/tex]
Playing with actual numbers I have always been able to see that they are indeed quite equal, yet algebraically I cannot prove it with arbitrary variables. I have been working on it for several days, and have tried expanding, completing the square, and everything else I can think of, but no luck