1.

If `x = 13 + 2sqrt(42)`, then `sqrt(x) + (1)/(sqrt(x))` is equal to `asqrt(b)` then find the value of `b - a` ?

Answer» Correct Answer - `5`
Given `x = 13 + 2sqrt(42)`
`x = 7 + 6 + 2sqrt(6 xx 7)`
`x = (sqrt(7) + sqrt(6))^(2)`
`:. sqrt(x) = sqrt(7) + sqrt(6)`
`(1)/(sqrt(x)) = (1)/(sqrt(7) + sqrt(6)) xx (sqrt(7) - sqrt(6))/(sqrt(7) - sqrt(6)) = (sqrt(7) - sqrt(6))/(7 - 6)`
`(1)/(sqrt(x)) = sqrt(7) - sqrt(6)`
`:. sqrt(x) + (1)/(sqrt(x)) = 2sqrt(7) = asqrt(b)`
`b = 7, a = 2`
`rArr b - a = 5`


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