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

1 Answer
Gió
Jul 25, 2015

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

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