Solve the equation.?

Question

x - 3 = sqrt(x - 1)

Answer 1

x - 3 = sqrt(x - 1)
(x - 3)^2 = sqrt(x - 1)^2
x^2 - 6x + 9 = x - 1
x^2 - 7x + 10 = 0
(x - 2)(x - 5) = 0
x = 2 and x = 5
Checking ...
x = 2
x - 3 = sqrt(x - 1)
2 - 3 = sqrt(2 - 1)
-1 = sqrt(1)
Nope
Checking ...
x = 5
x - 3 = sqrt(x - 1)
5 - 3 = sqrt(5 - 1)
2 = sqrt(4)
Yes
Only answer is 5.

Answer 2

Square both sides:

(x-3)^2 = x-1

x^2 - 6x + 9 = x - 1

Get zero on one side:

x^2 - 7x + 10 = 0

Factor: (x -5)(x - 2) = 0

x = 5 and x = 2

Check: 5 works, 2 does not since

2 - 3 = -1 and sqrt (2-1) = 1, so reject that solution, and

x = 5 is the only answer.

Answer 3

1st sqr both sides.... (x - 3)sqr = x - 1
(xsqr -6x + 9) = x -1
add 1 to both sides...xsqr - 6x +10 = x
minus x .......................xsqr - 7x +10 = 0
use quadratic equ. ....... (7+or- sqrt(49 - 40)) / (2)
A .... x= 5, x = 2
when u plug back in, only 5 works