Question

Question #b85b6

Answer 1

Solve a fourth-degree polynomial equation.

Explanation:

`sqrt{3 + x} + sqrt{2x - 1} = 5x \ge 1/2`

First, `x \ge 1/10`

Second, `sqrt{3 + x} = 5x - sqrt{2x - 1}`

`3 + x = (5x - sqrt{2x - 1})^2`

`3 + x = 25x^2 + 2x - 1 - 10xsqrt{2x - 1}`

`10xsqrt{2x - 1} = 25x^2 + x - 4`

`100x^2{2x - 1} = (25x^2 + x - 4)^2`

`200x^3 - 100x^2 = 625x^4 + x^2 + 16 + 50x^3 - 200x^2 - 8x`

`0 = 625x^4 - 150x^3 -99 x^2 - 8x + 16`

Here you can use Newton. Or test the fractions `n/d`

where `d` divides `625` and `n` divides `16`.

https://en.wikipedia.org/wiki/Newton%27s_method