Question

Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.

Answer 1

`(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