I cannot solve this!?

Question

sqrt x-1 = x-3
I cannot come up with a solution for this problem. Out of the two, neither one checks out.

Answer 1

I got x = 5

Answer 2

If you mean (sqrt(x)) - 1 = x-3 then
Add 1 to both sides and square:

x = (x-2)^2
x = x^2-4x+4
0 = x^2-5x+4

Factoring the right gives:

0 = (x-4)(x-1)

giving roots of 4 and 1. Substituting 4 shows that 4 is a solution, but substituting 1 shows that 1 is not a root to the equation - it is a spurious root, caused by squaring both sides.

One solution: x = 4.

Answer 3

For those who are saying that x=2 does not work, check again.

Sqrt(2-1) = 2-3
Sqrt(1) = -1
square both sides
1 = 1 tada!

the correct solution is x=2 or x=5 as was solved by at least a couple of people above

Answer 4

√(x - 1) = x - 3

Square both sides
x - 1 = x² - 6x + 9

by symmetric property,and by transposing,
x² - 6x + 9 - x + 1 = 0

We solve,
x² - 7x + 10 = 0

Thus we factor,
(x - 5)(x - 2) = 0

The only possible values of x is
x = 5 or x = 2

We check

√(x - 1) = x - 3

for x = 5,
√(5 - 1) =? 5 - 3
√4 =? 2
2 = 2 correct, so x = 5 is a solution

for x = 2,
√(2 - 1) =? 2 - 3
√1 =? -1
±1 = 1, if we allow negative sqrts, then x = 2 is a solution. but generally according to your equation the sqrt is principal (positive), so x = 2 cannot be a solution

SOLUTIONS:
x = 5
and if you will allow negative sqrt, then
x = 2.

But generally (THEaccepted answer), 2 cannoot be a solution

^_^

Answer 5

The above solutions are almost correct, If you try x=2, you get sqrt(2-1)=1 (not =) -1=2-3.

So 2 is not a solution. This is because the square root is always positive.

Answer 6

If you mean sqrt (x-1) = x -3,
by squaring both sides you get
x -1 = x^2 -6x +9
0=x^2-7x+10
0=(x-5)(x-2)
x=5 or x=2

Answer 7

(x-3)^2 = x-1; Therefore x^2-6x+9=x-1 giving x^2-7x+10=0; Thus (x-5)(x-2)=0; Solving gives x=5 or 2

Answer 8

sqrt(x - 1) = x - 3

square both sides

x - 1 = (x - 3)^2
x - 1 = (x - 3)(x - 3)
x - 1 = x^2 - 3x - 3x + 9
x - 1 = x^2 - 6x + 9
x^2 - 7x + 10 = 0
(x - 5)(x - 2) = 0

x = 5 or 2

Answer 9

x-1=(x-3)^2=x^2-6x+9
x^2-7x+10=0
(x-5)(x-2)=0
x=5, 2

2 doesn't check: 1!=-1
5 checks: 2=2

5

Answer 10

square both sides

x=5 or x=2