Question

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

Answer 1

Answer:

8 root 3

Step-by-step explanation:

if x = 2 + root 3

1/x = 1/ 2 + root 3

on rationalising we get

1/x = 2 - root 3

Now (x)^2 = (2 + root3 )^2

= (2)^2 +(root3)^2 + 2(2)(root 3)

= 4 + 3 + 4root3

= 7 + 4 root 3

same as (1/x)^2 = (2 -root 3)^2

= 7 - 4root 3

Now x^2 - 1/x^2

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

= 7 + 4 root 3 - 7 + 4 root 3

= 8 root 3