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`

Applying componendo and dividendo we get

`(x^4 + 1 + 2x^2)/(x^4 + 1 - 2x^2) = (17 + 8)/(17 - 8)`

`=> ((x^2)^2 + (1)^2 + 2 xx x^2 + 1)/((x^2)^2 + (1)^2 - 2 xx x^2 xx 1) = 25/9`

`=> (x^2 +  1)^2/(x^2 - 1)^2 = 5^2/3^2`

`=> ((x^2 + 1)/(x^2 - 1))^2 = (5/3)^2`

`=> (x^2 + 1)/(x^2 - 1) = 5/3`

Applying componeddo and diividendo we get

`(x^2 + 1 + x^2 - 1)/(x^2 + 1 - x^2 + 1) = (5 + 3)/(5 - 3)`

`=> (2x^2)/2 = 8/2`

`=> x^2 = 4`

`=> x = +- 2`