Question

if x=3+√8 find the value of [x²+1/x²]

Answer 1

x = 3 + √8

x² = (3+ √8)² = 9 + 8 + 6√8 = 17 + 6√8

 1     =           1            =         17 -  6√8              =           17 - 6√8    

x²           17 + 6√8          (17 + 6√8) (17 - 6√8)            (17)² - (6√8)

=     17 - 6√8       = 17 - 6√8

     289 - 288

x²   +     1       =   17 + 6√8 + 17 - 6√8 = 34

             x²

Answer 2

Answer:

         x²+ 1 / x² = 34

             x²- 1 / x² = 12√8

Step-by-step explanation:

x = 3+ √8

1 / x = 1 / (3+√8)

rationalizing

1 / x = 1 × (3-√8) / (3+√8) × (3-√8)

1 / x = (3-√8) / (3²-√8²)

1 / x = (3-√8) / 9 - 8

1 / x = (3-√8) / 1

1 / x = (3-√8)  

Put the value and find out

x² + (1 / x²)

So x² + 1/ x² = (3 +√8)² + (3 -√8)²

= 9+ 6√8 + 8 + 9– 6√8 + 8

= 34. Ans.

x² - (1 / x²)  

So x² - 1/ x² = (3 +√8)² - (3 -√8)²

= 9+ 6√8 + 8 -( 9– 6√8 + 8)

= 9+ 6√8 + 8 - 9 + 6√8 - 8)

= 12√8. Ans