Question

If x=9-4√5 then X+1/x
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Answer 1

Answer:

18

Step-by-step explanation:

Here,

⇒ x = 9 - 4√5

    Reciprocal of x should be:

⇒ 1 / x = 1 / (  9 - 4√5 )

    Multiply as well as divide RHS by 9 + 4√5:

⇒ 1 / x = ( 9 + 4√5 ) / ( 9 - 4√5 )( 9 + 4√5 )

     Using ( a + b )( a - b ) = a^2 - b^2 for denominator of RHs

⇒ 1 / x = ( 9 - 4√5 ) / [ ( 9 )^2 - ( 4√5 )^2 ]

⇒ 1 / x = ( 9 - 4√5 ) / ( 81 - 80 )

⇒ 1 / x = ( 9 - 4√5 ) / 1

⇒ 1 / x = 9 - 4√5

       Hence,

⇒ x + 1 / x

⇒ 9 + 4√5 + ( 9 - 4√5 )

⇒ 9 + 4√5 + 9 - 4√5

⇒ 9 + 9

⇒ 18