It it true that is ${a^2+c^2\over b^2+d^2}=1$ for $ad-bc=1$?
I tried substituting in $a={1-bc\over d}$ but it is still a mess.
(How do you ask Wolfram Alpha a question like this where we ask it to calculate something with an imposed condition?)
It it true that is ${a^2+c^2\over b^2+d^2}=1$ for $ad-bc=1$?
I tried substituting in $a={1-bc\over d}$ but it is still a mess.
(How do you ask Wolfram Alpha a question like this where we ask it to calculate something with an imposed condition?)
It's not true. Try it for $a = 2$ and $b = c = d = 1$:
$ ad - bc = 2\times1 - 1\times1 = 1 $
$ \frac{a^2+c^2}{b^2+d^2} = \frac{2^2+1^2}{1^2+1^2} = \frac{5}{2} \ne 1 $
As for WA, you can use the FullSimplify
function to simplify an expression given some assumptions. Here is an example.