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Question
Using properties of proportion, solve for x:
`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`
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Solution
`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`
Applying componendo and dividendo,
`(3x + sqrt(9x^2 - 5) + 3x - sqrt(9x^2 - 5))/(3x + sqrt(9x^2 - 5) - 3x + sqrt(9x^2 - 5)) = (5 + 1)/(5 - 1)`
`(6x)/(2sqrt(9x^2 - 5)) = 6/4`
`(3x)/sqrt(9x^2-5) = 3/2`
`x/sqrt(9x^2 - 5) = 1/2`
Squaring both sides,
`x^2/(9x^2 - 5) = 1/4`
`4x^2 - 9x^2 = - 5`
`-5x^2 = -5`
`5x^2 = 5`
`x^2 = 1`
`x= sqrt1`
x = 1
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