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Question
Find x from the following equations : `(sqrt(x + 4) + sqrt(x - 10))/(sqrt(x + 4) - sqrt(x - 10)) = (5)/(2)`
Solution
`(sqrt(x + 4) + sqrt(x - 10))/(sqrt(x + 4) - sqrt(x - 10)) = (5)/(2)`
Applying componendo and dividendo,
`(sqrt(x + 4) + sqrt(x - 10) + sqrt(x + 4) - sqrt(x - 10))/(sqrt(x + 4) + sqrt(x - 10) - sqrt(x + 4) + sqrt(x - 10)) = (5 + 2)/(5 - 2)`
⇒ `(2sqrt(x + 4))/(2sqrt(x - 10)) = (7)/(3)`
⇒ `(sqrt(x + 4))/(sqrt(x - 10)) = (7)/(3)`
Squaring both sides,
`(x + 4)/(x - 10) = (49)/(9)`
⇒ 49x – 490 = 9x + 36
⇒ 49x – 9x = 36 + 490x
⇒ 40x = 526
∴ x = `(526)/(40)`
= `(263)/(20)`.
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