Question

If x is equal to 2 + root 3 find the value of x squared plus 1 by x square

Answer 1

x = 2 + √3

x² = (2+√3)²

= (2)² + 2x2x√3 + (√3)²

=4 + 4√3 + 3

=7 + 4√3

1/x² = 1/7 + 4√3 x 7 - 4√3/7 - 4√3

= 7 - 4√3/ (7)² - (4√3)²

= 7 - 4√3/49-48

=7-4√3

therefore, x²+1/x² is

7 + 4√3 + 7-4√3

= 14

so your required answer is 14

thank you

Answer 2

See the attachment for detail solution
Hope it will help you