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Questions
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Using properties of proportion, find the value of x from the following:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
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Solution
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
⇒ `(2x + sqrt(4x^2 -1) + 2x - sqrt(4x^2 - 1))/(2x + sqrt(4x^2 - 1) - 2x + sqrt(4x^2 - 1)) = (4+1)/(4-1) ` (By componendo dividendo)
⇒ `(4x)/(2sqrt(4x^2 -1)) = 5/3`
⇒ `(2x)/(sqrt(4x^2 -1)) = 5/3`
Squaring both sides,
⇒ `((2x)/sqrt(4x^2 - 1))^2 = (5/3)^2`
⇒ `(4x^2)/(4x^2 -1) = 25/9`
⇒ 9(4x2) = 25(4x2 − 1)
⇒ 36x2 = 100x2 − 25
⇒ 64x2 = 25
⇒ x2 = `25/64`
⇒ x = `5/8`
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