Question

If x is 2+ root 3 then find (x^2+1/x^2) (x^2-1/x^2)

Answer 1

Here x=2−3–√ ................…………………………………….....(1)

Hence 12−3√=12−3√⋅2+3√2+3√=2+3–√ .....................(2)

From (1) and (2) we get x+1x=4 .......……………………………....(3)

and x−1x=−23–√ ...............…………………….………....(4)

From (3) and (4) we get x2−1x2=(x+1x).(x−1x)=−83–√.

Hoped I helped