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

1 Answer
Jul 25, 2015

Answer:

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#