Question

If x+1 upon x =under root 5 ,find x square +1 upon x square

Answer 1

Step-by-step explanation:

Given that

x = 2 + √5

x^2 + 1/x^2 = ?

Solution

1/x = 1/2 + √5

By rationalization

= 1 × (2 - √5)/(2 + √5) × (2 - √5)

= 2 - √5/(2)^2 - (√5)^2

= 2 - √5/4 - 5

= 2 -√5/-1

= -2 + √5

Therefore ,

x^2 + 1/x^2

= (2 + √5)^2 + (-2 + √5)^2

= (2)^2 + (√5)^2 + 2 × 2 × √5 + (-2)^2 + (√5)^2 + 2 × (-2) × √5

= 4 + 5 + 4√5 + 4 + 5 - 4√5

= 9 + 4√5 + 9 - 4√5

= 18