Question

If x = 3+√8, find the value of x² + 1/x² .

Answer 1

Given :  x = 3 + √8

 

To find : value of x² +  1/x² .

We have , x = 3 +√8

∴ 1/x = 1/(3 +√8)

On Rationalising the denominator :  

1/x = 1 × (3 -√8)/ [(3 +√8) × (3 -√8)]

1/x = (3 -√8)/[3² - √8²]

[By Using Identity : (a + b)(a – b) = a² - b²]

1/x = (3 - √8)/[9 - 8]

1/x = 3 - √8/1

1/x = 3 - √8

Thus, x + 1/x =  (3 + √8) + (3 - √8)

x + 1/x = 3 + √8 + 3 - √8

x + 1/x = 6

We know that, x² + (1/x)² = (x + 1/x)² - 2

x² + 1/x²  = 6² - 2

x² + 1/x² = 36 - 2

x² + 1/x² = 34

Hence the value of  x² + 1/x²  is 34 .

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Step-by-step explanation:

GIVEN,

x = 3+ √8

we given the task

x² + 1/x²

solving the equation

Putting the value

x = (3+√8)(3-√8) / (3-√8)+(3 -√8)²

x = (9 -8) / (3-√8)+(3 -√8)²

x = 1/ (3 -√8)+(3 -√8)²

x = 9+6√8+8 + 9–6√8+8

x = 34. Ans.