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Question
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
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Solution
`(x^4 + 1)/(2x^2) = 17/8`
Using componendo and dividendo,
If `a/b = c/d`
`(x^4 + 1 + 2x^2)/(x^4 + 1 - 2x^2) = (17 + 8)/(17 - 8)`
`=> (x^2 + 1)^2/(x^2 - 1)^2 = 25/9`
`=> ((x^2 + 1)/(x^2 - 1)) = (5/3)^2`
`=> (x^2 + 1)/(x^2 - 1) = 5/3`
⇒ 3(x2 + 1) = 5(x2 − 1)
⇒ 3x2 + 3 = 5x2 − 5
5x2 − 3x2 = 3 + 5
2x2 = 8
x2 = 4
x = `+- sqrt4`
x = ± 2
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