√x - 1 = x - 3 Solve.?

Question

Could someone give me a hand with this one. Thank you so much!

Solve.

√x - 1 = x - 3

Answer 1

x^1/2 - 1 = x - 3
=> x^1/2 = x - 3 + 1
=> x^1/2 = x - 2
Square the both sides
=> x =(x - 2)^2
=> x = x^2 - 4x + 4
=> x + 4x = x^2 + 4
=>5x = x^2 + 4
=>=x^2-5x+4
=>=(x-4)(x-1)
=>x = 4 : x = 1
So, solution is 4

Answer 2

√x - 1 = x - 3
√x = x - 2
(√x)² = (x - 2)²
x = x² - 4x + 4
0 = x² - 5x + 4
0 = (x - 4)(x - 1)
x = 4 or x = 1
but squaring both sides can introduce extraneous solutions, so we check

√4 - 1 = 4 - 3
2 - 1 = 1 yes

√1 - 1 = 1 - 3
0 = -2 no

so solution is x = 4

Answer 3

square root of x = x-3+1
square roof of x = x-2
square both sides of the equation
x = (x-2)^2
x = x^2-4x+4
= x^2-4x-x+4
= x^2-5x+4
(x-4)(x-1)
x = 4: x = 1
the answer is x = 4

Answer 4

assuming that the given equation is

sqrt(x-1) = x-3

squaring

x-1 = (x-3)^2

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

x^2 -7x + 10 = 0

x^2 - 5x - 2x + 10 = 0

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

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

x = 5 or 2

Answer 5

That problem has an infinite amount of answers.