Question

If x =3-√8 , evaluate x+1/x

Answer 1

Step-by-step explanation:

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Given , x = 3 - √8

(I) x + ( 1 / x ) = ?

=> (3 - √8) + (1 / 3 - √8 )

=> (3 - √8) + { ( 3 + √8 ) / (3 + √8 ) (3 - √8) }

=> (3 - √8) + { ( 3 + √8 ) / ( 9 - 8) }

=> 3 - √8 + 3 + √8

=> 6

Ans. => x + ( 1 / x ) = 6

Given , x = 3 - √8

(II) x² + ( 1 / x²) = ?

=> (3 - √8)² + (1 / 3 - √8 )²

=> ( 9 - 8) + { 1 / (9 - 8)}

=> 1 + 1 / 1

=> 1 + 1

=> 2

Ans. => x² + ( 1 / x²) = 2

Given , x = 3 - √8

(III) x² - ( 1 / x²) = ?

=> (3 - √8)² - (1 / 3 - √8 )²

=> ( 9 - 8) - { 1 / (9 - 8)}

=> 1 - 1 / 1

=> 0

Ans. => x² - ( 1 / x²) = 0

Answer 2

Step-by-step explanation:

{\huge{\boxed{\sf{\pink{☞Answe࿐★}}}}}☞Answe࿐★

Given , x = 3 - √8

(I) x + ( 1 / x ) = ?

=> (3 - √8) + (1 / 3 - √8 )

=> (3 - √8) + { ( 3 + √8 ) / (3 + √8 ) (3 - √8) }

=> (3 - √8) + { ( 3 + √8 ) / ( 9 - 8) }

=> 3 - √8 + 3 + √8

=> 6

Ans. => x + ( 1 / x ) = 6

Given , x = 3 - √8

(II) x² + ( 1 / x²) = ?

=> (3 - √8)² + (1 / 3 - √8 )²

=> ( 9 - 8) + { 1 / (9 - 8)}

=> 1 + 1 / 1

=> 1 + 1

=> 2

Ans. => x² + ( 1 / x²) = 2

Given , x = 3 - √8

(III) x² - ( 1 / x²) = ?

=> (3 - √8)² - (1 / 3 - √8 )²

=> ( 9 - 8) - { 1 / (9 - 8)}

=> 1 - 1 / 1

=> 0

Ans. => x² - ( 1 / x²) = 0

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