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If x=3+2sqrt2, find the value of (x^2+1/...

If `x=3+2sqrt2,` find the value of `(x^2+1/x^2), `

A

`37`

B

`35`

C

`34`

D

`36`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `x = 3 + 2sqrt(2)`
`therefore (1)/(x) = (1)/((3 + 2sqrt(2))) = (1)/((3+ 2sqrt(2)) xx((3-2sqrt(2))/((3-2sqrt(2)))))`
`= ((3-2sqrt(2)))/((3)^(2) - (2sqrt(2))^(2)) = ((3-2sqrt(2)))/( (9-8 )) = 3-2sqrt(2)`
`therefore x + (1)/(x) = (3+ 2sqrt(2)) + (3- 2sqrt(2)) = 6`
`rArr (x+(1)/(2)) ^(2) = 6^(2) = 36`
`rArr x^(2) + (1)/(x^(2)) + 2 xx x xx (1)/(x) = 36`
`rArr (x^(2) +(1)/(x^(2)))+ 2= 36 rArr(x^(2) +(1)/(x^(2))) = 36- 2 = 34`
Hence `(x^(2) +(1)/(x^(2))) = 34`
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