## Proving an expression is perfect square

I have this expression I got in one larger exercise: (2+√3)2n+1+(2−√3)2n+1−46(2+√3)2(n+1)+1+(2−√3)2(n+1)+1−46+1 and i need to prove it is perfect square. I tried many different approaches but couldn’t find way to show it is square. Interesting fact is (2+√3)(2−√3)=1 so I tried replacing (2+√3)=x and (2−√3)=1/x to see if I would get an idea. Alternative form … Read more