Question

HELP?!!!! 10 POINTS!!!

Answer 1

Answer:

It is the third one

I took the test XD

Step-by-step explanation:

Answer 2

Answer:

There is only one solution: x=10

The solution x=4 is an extraneous solution.

Step-by-step explanation:

We have this equation:

$\sqrt{2x-4} -x+6=0$

Let's solve for x:

Add x to both sides:

$\sqrt{2x-4} -x+x+6=0+x\\\sqrt{2x-4}+6=x$

Subtract 6 from both sides:

$\sqrt{2x-4}+6-6=x-6\\\sqrt{2x-4}=x-6$

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 $x_1$ :

$\sqrt{2*10-4} -10+6=0\\4-10+6=0\\0=0$

This solution is correct.

Evaluating $x_2$ :

$\sqrt{2*4-4} -4+6=0\\2-4+6=0\\4=0$

So this solution is incorrect.

Therefore:

There is only one solution: x=10

The solution x=4 is an extraneous solution.