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यदि `x=5-sqrt(21)` है तो `(sqrt(x))/(sqrt(32-2x)-sqrt(21))` का मान क्या होगा?A. `1/(sqrt(2))(sqrt(3)-sqrt(7))`B. `1/(sqrt(2)(sqrt(7)-sqrt(3))`C. `1/(sqrt(2)(sqrt(7)+sqrt(3))`D. `1/(sqrt(2))(7+sqrt(3))`

Answer» Correct Answer - B
`x=5-sqrt(21)`
`2x=10-2sqrt(21)`…………….i
`implies2x=(sqrt(7))^(2)+(sqrt(3))^(2)-2(sqrt(7))(sqrt(3))`
`implies 2x=(sqrt(7)-sqrt(3))^(2)`
`implies x=1/2(sqrt(7)-sqrt(3))^(2)`
` implies sqrt(x)=1/(sqrt(2))sqrt((sqrt(7)-sqrt(3))^(2))` ltbgt `=1/(sqrt(2))(sqrt(7)-sqrt(3))`
`:. (sqrt(x))/(sqrt(32-2x)-sqrt(21))`
`(sqrt(7)-sqrt(3))/(sqrt(2)(sqrt(32-(10-2sqrt(21)))-sqrt(21)))`
`=(sqrt(7)-sqrt(3))/(sqrt(2)(sqrt(22+2sqrt(2))-sqrt(21)))`
`= (sqrt(7)-sqrt(3))/(sqrt(2)(sqrt((sqrt(21)+1)^(2))-sqrt(21)))`
`=(sqrt(7)-sqrt(3))/(sqrt(2)(sqrt(21a)+1-sqrt(21)))`
`=((sqrt(7)-sqrt(3)))/(sqrt(2))`


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