Question

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Answer 1

Step-by-step explanation:

please check your answer in the attachment ...

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Answer 2

Answer:

34, 1154

Step-by-step explanation:

Given,

      x = 3 + √8

⇒ x = 3 +√8

⇒ 1 / x = ( 3 + √8 )

Multiplying and dividing RHS by ( 3 - √8 ):

⇒ ( 1 / x ) = ( 3 - √8 ) / ( 3 + √8 )( 3 - √8 )

⇒ 1 / x = ( 3 - √8 ) / [ ( 3 )^2 - ( √8 )^2 ]         { Using ( a + b )( a - b ) = a^2 - b^2 }

⇒ 1 / x = ( 3 - √8 ) / 1

⇒ 1 / x = 3 - √8

Therefore,

⇒ x^2 + 1 / x^2

⇒ ( 3 + √8 )^2 + ( 3 - √8 )^2

⇒ 3^2 + ( √8 )^2 + 6√8 + 3^2 + ( √8 )^2 - 6√8

⇒ 9 + 8 + 9 + 8

⇒ 17 + 17

⇒ 34

⇒ x^2 + 1 / x^2 = 34

⇒ ( x^2 + 1 / x)^2 = 34^2

⇒ x^4 + 1 / x^4 + 2( x^2 )( 1 / x^2 ) = 34^2

⇒ x^4 + 1 /x^4 = 1154