Question

Ans of question no 11

Answer 1

Given:-

x= 3+√8

To find:-

x^2+1/x^2

Solution:-

x= 3+√8

1/x=1/3+√8

1/x= 1/3+√8×3-√8/3-√8 [ on rationalising ]

1/x= 3-√8

now x+1/x= 3+√8+3-√8

= 6

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

(6)^2= x^2+1/x^2+2

36-2= x^2+1/x^2

so x^2+1/x^2= 34

hope it helps you

please mark brainliest

Answer 2

Step-by-step explanation:

x = 3 + √8

to evaluate x²+1/x²

first take reciprocal of x,

1/x = 1/(3+√8)

now rationalise the denominator

1/x = 1/3+√8 × (3-√8)/(3-√8)

=> 1×(3-√8)/(3+√8)(3-√8)

=> (3-√8)/3² - (√8)²

=> (3-√8)/9 - 8

=> 3-√8/1

=> 3 - √8

now x = 3+√8 and 1/x = 3-√8

add x and 1/x

x + 1/x = 3+√8+3-√8

=> 6 [ √8 cancels out ]

x+1/x = 6

square both sides

(x+1/x)² = 36

=> x² + 1/x² + 2*x*1/x = 36

=> x² + 1/x² + 2 = 36 [ x cancels out ]

=> x² + 1/x² = 36 - 2

=> x² + 1/x² = 34