Question

if X equal to 2 + root 3 find the value of x square + 1 by x square​

Answer 1

According to the question

x = 2 + √3

x² + 1/x² = ?

Now answer

x² = (2+√3)²

= 4 + 3 + 4√3 = 7 + 4√3

1 1

—— = —————

x² 7+4√3

by rationalisation

1 7-4√3

————— × —————

7+4√3 7-4√3

= 7-4√3

————————

(7)² - (4√3)² [ by using (a+b) (a-b) = a² - b² ]

7-4√3 7-4√3

————— = ————— = 7-4√3

49 - 48 1

x² + 1/x² = 7+4√3 + (7-4√3)

= 7 + 4√3 + 7 - 4√3

= 14