Question

If x = `(4 - sqrt(15))`, find the values of 

`x^2 + (1)/x^2`

Answer 1

`x^2 + (1)/x^2`

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

we will first find the value of `x + (1)/x`

`x + (1)/x = (4 - sqrt(15)) + (1)/((4 - sqrt(15))`

= `((4 - sqrt(15))^2 + 1)/((4 - sqrt(15))`

= `(16 + 15 - 8sqrt(15) + 1)/((4 - sqrt(15))`

= `(8(4 - sqrt(15)))/((4 - sqrt(15))`

= 8

substituting the valuesin (1)
`(x^2 + (1)/x^2) = (x + (1)/x)^2 -2`
= 8² - 2
= 64 - 2
= 62
`(x^2 + (1)/x^2)`  = 62