1.

यदि `x=sqrt(3)+1/(sqrt(3))` हो तो `(x-(sqrt(126))/(sqrt(42))) (x-1/(x-(2sqrt(3))/3))` का मान क्या है?A. `5 (sqrt(3))/6`B. `(2sqrt(3))/3`C. `5/6`D. `2/3`

Answer» Correct Answer - C
`x=sqrt(3)+1/(sqrt(3))=(3+1)/(sqrt(3))=4/(sqrt(3))`
So `(x-(sqrt(126))/(sqrt(42)))(x-1/(x-(2sqrt(3))/3))`
`=(4/(sqrt(3))-(sqrt(126))/(sqrt(42)))(x-1/(4/(sqrt(3))-2/(sqrt(3))))`
`=((4sqrt(42)-sqrt(126)xxsqrt(3))/(sqrt(3)xxsqrt(142)))(x-1/(2//sqrt(3)))`
`=(4sqrt(42)-3sqrt(42))/(sqrt(3)xx sqrt(42))(x-(sqrt(3))/2)`
`=(4sqrt(42)-3sqrt(42))/(sqrt(3)xxsqrt(42))(4/(sqrt(3))-(sqrt(3))/2)`
`=((sqrt(42))/(sqrt(3)xxsqrt(42)))((8-3)/(2sqrt(3)))=5/6`


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