Question

HELP?!!!! 10 POINTS!!!

Which statement best reflects the solution(s) of the equation?

√2x−4−x+6=0

Answer 1

It is the third one

I took the test XD

Explanation:

Answer 2

There is only one solution: x=10

The solution x=4 is an extraneous solution.

Explanation:

We have this equation:

`√(2x-4) -x+6=0`

Let's solve for x:

Add x to both sides:

`√(2x-4) -x+x+6=0+x\\√(2x-4)+6=x`

Subtract 6 from both sides:

`√(2x-4)+6-6=x-6\\√(2x-4)=x-6`

Raise both sides to the power of two:

`2x-4=(x-6)^2`

Expand out the terms of the right side:

`2x-4=x^2-12x+36`

Subtract 2x from both sides and add 4 to both sides:

`x^2-14x+40=0`

Factor into a product:

`(x-10)(x-4)=0`

So the solutions are:

`x_1=10\\x_2=4`

Evaluating
`x_1` :

`√(2*10-4)  -10+6=0\\4-10+6=0\\0=0`

This solution is correct.

Evaluating
`x_2` :

`√(2*4-4)  -4+6=0\\2-4+6=0\\4=0`

So this solution is incorrect.

Therefore:

There is only one solution: x=10

The solution x=4 is an extraneous solution.