Question

if x= 2+ √3 then x^2+ 1/x^2 =?​

Answer 1

if x= 2+sqrt3

then

1/x=2-sqrt3 (by rationaliztion)

then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(1/X)

that is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+2

4^2 -2=x^2+(1/x)^2

i.e, 14 is the answer