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Question
Using componendo and idendo, find the value of x
`(sqrt(3x + 4) + sqrt(3x - 5))/(sqrt(3x + 4) - sqrt(3x - 5)` = 9
Solution
`(sqrt(3x + 4) + sqrt(3x - 5))/(sqrt(3x + 4) - sqrt(3x - 5)) = (9)/(1)`
Using componendo and dividendo
`(sqrt(3x + 4) + sqrt(3x - 5) + sqrt(3x + 4) - sqrt(3x - 5))/(sqrt(3x + 4) + sqrt(3x - 5) - sqrt(3x + 4) + sqrt(3x - 5))`
= `(9 + 1)/(9 - 1) = (10)/(8) = (5)/(4)`
`(2sqrt(3x + 4))/(2sqrt(3x - 5)) = (5)/(4)`
⇒ `(3x + 4)/(3x - 5) = (25)/(16) ...("squaring both sides")`
48x + 64 = 75x - 125
⇒ 75x - 48x = 125 + 64
27x = 189
⇒ x = `(189)/(27)`
= 7.
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