Question

How do you solve `sqrt(x - 3) + 1 = x`?

Answer 1

I found:
`x_1=(3+isqrt(7))/2`
`x_2=(3-isqrt(7))/2`

Explanation:

I would write it as:
`sqrt(x-3)=x-1`
square both sides:
`x-3=(x-1)^2` rearrange:
`x-3=x^2-2x+1`
`x^2-3x+4=0`
Solving with the Quadratic Formula you get:
`x_(1,2)=(3+-sqrt(9-16))/2=(3+-sqrt(-7))/2=`
using the imaginary unit: `sqrt(-1)=i` you get two solutions:
`x_1=(3+isqrt(7))/2`
`x_2=(3-isqrt(7))/2`