Question

If x =2+√3, find the value of x^2+1/x^2

Answer 1

Answer:

x= 2+√3

1/x= 1/ 2+√3

We have to rationalize

=1/ 2+√3 * 2-√3/2-√3

= 2-√3/ 4-3

= 2-√3

1/x= 2-√3

x^2+1/x^2

= (2+√3)^2+ (2-√3)^2

= 4+3+2(2)(√3)+ 4+3-2(2)+√3)

=(7+4√3)+ (7-4√3)

=7+4√3+7-4√3

=14

Therefore the answer is 14

Thank you