Question

Q3. If x= √6 + √5, then find the value of
(i) 1/x. (ii) x+ 1/x (iii) (x^2+1/x^2) (iv) X- 1√x


pls answer each .pls fast​

Answer 1

Step-by-step explanation:

Given :

( x + 1 /x ) = 5

We need to find x2 + 1 / x2

( x + 1 / x )2 = 25

= x2 + 1 / x2 + 2 (x)(1/x) = 25

= x2 + 1/x2 + 2 = 25

= x2 + 1 / x2 = 25 – 2

= x2 + 1 / x2=23

Hence x2 + 1 / x2 = 23

Answer 2

Answer:

14

Step-by-step explanation:

2 + √3

1/x = 1/2 + √3

= 1 × (2-√3)/(2 + √3)(2-√3)

= (2-√3)/(2^2-√3^2)

= (2-√3)/4 - 3

= (2-√3)

Therefore,

x^2 = (2+√3)

= (2)^2 + (√3)^2 + 2 × 2 × √3

= 4 + 3 + 4√3

= 7+ 4√31/x^2 = (2-√3)^2

= (2)^2 + (√3)^2 - 2 × 2 × √3

= 4 + 3 - 4√3

= 7 - 4√3

x^2+1/x^2

= (7 + 4√3) + (7 - 4√3)

= 7+ 4√3 +7-4√3

= 7 + 7 + 4√3 - 4√3

= 14