1.

यदि `x=(sqrt(3))/2` है तो `(sqrt(1+x))/(1+sqrt(1+x))+(sqrt(1-x))/(1-sqrt(1-x)` किसके बराबर होगा?A. 1B. `2//sqrt(3)`C. `2-sqrt(3)`D. `2`

Answer» Correct Answer - B
`x=(sqrt(3))/2`
or `1+x=1+(sqrt(3))/2=(2+sqrt(3))/2`
`=(2(2+sqrt(3)))/(2xx2)`
(divides and multiply by 2)
`implies 1+x=(4+2sqrt(3))/4`
`=(1+3+2sqrt(3))/4`
`=((1)^(2)+(sqrt(3))^(2)+2xx1xxsqrt(3))/4`
`1+ximplies((1+sqrt(3))^(2))/4`
`:.sqrt(1+x)=(1+sqrt(3))/2`
Similarly,
`sqrt(1-x)implies(sqrt(3)-1)/2`
`:. (sqrt(1-x))/(1+sqrt(1+x))+(sqrt(1-x))/(1-sqrt(1-x))`
`=((1+sqrt(3))/2)/(1+(1+sqrt(3))/2)+((sqrt(3)-1)/2)/(1-(sqrt(3)-1)/2)`
`implies (1+sqrt(3))/(3+sqrt(3))+(sqrt(3)-1)/(3-sqrt(3))`
`= (1+sqrt(3))/(sqrt(3)(sqrt(3)+1))+(sqrt(3)-1)/(sqrt(3)(sqrt(3)-1))`
`=1/(sqrt(3))+1/(sqrt(3))=2/(sqrt(3))`


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