Question

How do you solve for x in `1/x + x = 4`?

Answer 1

Refer to explanation

Explanation:

First the equation holds for `R-{0}`.Multiply with x both parts of equation you get

`x*(1/x+x)=4*x=>1+x^2=4x=>x^2-4x+1=0=>`

This is a trinomial with roots given by

`x_1,_2=(-b+-sqrt(b^2-4ac))/(2a)`

where `a=1,b=-4,c=1`

So the roots are
`x_1=2-sqrt3` and `x_2=2+sqrt3`

Both roots are acceptable since they belong to `R-{0}`