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,

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