Question

If x =3-√8 then find the value of(a) x+1/x (b)x²+1/x²​

Answer 1

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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