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