1.

If `x=(1)/(sqrt(3)+2)`, then `(x+(1)/(x))^(2)`=______A. 16B. 3C. 12D. 6

Answer» Correct Answer - A
Given that `x=(1)/(sqrt(3)+2)`
`implies x=(2-sqrt(3))/((2+sqrt(3))(2-sqrt(3)))`
`implies x=(2-sqrt(3))/(4-3)`
`implies x=2-sqrt(3)`
And `(1)/(x)=sqrt(3)+2`
Now `(x+(1)/(x))^(2)=(2-sqrt(3)+sqrt(3)+2)^(2)`
`=(4)^(2)=16`


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