Question

What is the solution for the equation x-fx-1=3?A. X = 5 only, because x = 2 is extraneous.B. No solution, because x = -5 and x = -2 are both extraneous.C. X = 2 only, because x = 5 is extraneous.D. x= 2 or x = 5

Answer 1

Question:

Solution:

Consider the following expression:

`x-\sqrt[]{x-1}=3`

solving for the square root, we get:

`x-3=\sqrt[]{x-1}`

now, squaring both sides of the equation we remove the square root, then we get:

`(x-3)^2=x-1`

Expanding the left side of the equation, we get:

`x^2-6x+9^{}=x-1`

this is equivalent to:

`x^2-7x+10^{}=0`

Solving this quadratic equation by the quadratic formula, we get:

`x=\text{ 5 or x=2}`

but, notice that for x= 2 we have that:

`2-\sqrt[]{2-1}=2-1=1\text{ }\\e3`

and for x= 5 we obtain that:

`5-\sqrt[]{5-1}=5-\sqrt[]{4}\text{ = 5-2 = 3}`

So that, we can conclude that the correct answer is:

x= 5 only, because x=2 is extraneous.