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Question
Using the properties of proportion, solve for x, given.
`(x^4 + 1)/(2x^2) = (17)/(8)`.
Solution
`(x^4 + 1)/(2x^2) = (17)/(8)`
Using Componendo and Dividendo
`(x^2 + 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) ...("taking square root on both the sides")`
Again applying Componendo and Dividendo
`(x^2 + 1 + x^2 - 1)/(x^2 + 1 - x^2 + 1) = (5 + 3)/(5 - 3)`
`(2x^2)/(2) = (8)/(2)`
⇒ x2 - 4
⇒ x = ±2.
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