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प्रश्न
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
उत्तर
`(x^4 + 1)/(2x^2) = 17/8`
Using componendo and dividendo,
`(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`
`=> (x^2 + 1 + x^2 - 1)/(x^2 + 1 - x^2 + 1) = (5 + 3)/(5 -3)` ...(Using componendo and dividendo)
`=> (2x^2)/2 = 8/2`
`=>` x2 = 4
`=>` x = ±2
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