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प्रश्न
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
उत्तर
`(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`
`=> (4x^2)/(4x^2 -1) = 25/9` (squaring both sides)
`=>(4x^2 - 4x^2 + 1)/(4x^2 -1) = (25-9)/9` (By dividendo)
`=> 1/(4x^2 -1) = 16/9`
`=> 9 = 64x^2 - 16`
`=> 64x^2 = 25`
`=> x^2 = 25/64`
`=> x = +- 5/8`
`=> x = 5/8` (x is positive)
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