Question

Please help me solve this problem
...see post below.

Answer 1

\[x-1=\sqrt{x^4-2x^3}/x^2-4\]

Answer 2

@Destinymasha @golden_bullets @phi @mathmale @Preetha

Answer 3

@Hero @amistre64 @Zarkon

Answer 4

Is it:

\[x - 1 = \sqrt{\frac{x^4 - 2x^3}{x^2 - 4}}\]


or is it:

\[x - 1 = \frac{\sqrt{x^4 - 2x^3}}{x^2 - 4}\]

Answer 5

no actually you are right with the first one, it is all under the square root

Answer 6

Okay, if that's the case, then you should begin by squaring both sides:

\((x - 1)^2 = \left(\sqrt{\dfrac{x^4 - 2x^3}{x^2 - 4}}\right)^2\)

Answer 7

Square root and square will cancel, leaving you with:

\((x-1)^2 = \dfrac{x^4 - 2x^3}{x^2 - 4}\)


At this point you should expand the left side and factor the right side:

\((x - 1)(x - 1) = \dfrac{x^3(x - 2)}{(x + 2)(x - 2)}\)

Obviously the (x - 2)'s cancel leaving you with:
\((x - 1)(x-1) = \dfrac{x^3}{(x + 2)}\)

Answer 8

Can you finish the rest from there?

Answer 9

would i foil the (x-1)(x-1)

Answer 10

nevermind you just unfoiled it

Answer 11

so what do you do next?

Answer 12

Actually, you want to continue expanding:
\((x + 2)(x - 1)(x - 1) = x^3\)

Answer 13

I would multiply in the following manner:
\((x + 2)(x(x - 1) -1(x - 1) = x^3\)
\((x + 2)(x^2 - x - x + 1) = x^3\)
\((x + 2)(x^2 - 2x + 1) = x^3\)

Answer 14

so you multiplied both sides by the (x+2) and now you have to get rid of the exponential three. do you need to simplify the x^3 further?

Answer 15

\(x^3\) can't be simplified any further.

Answer 16

I'm basically showing you what to do from here.

Answer 17

Continue expanding:
\(x(x^2 - 2x + 1) + 2(x^2 - 2x + 1) = x^3\)
\(x^3 - 2x^2 + x + 2x^2 - 4x + 2 = x^3\)
\(x^3 + (2x^2 - 2x^2) + (x - 4x) + 2 = x^3\)

Answer 18

At this point you can subtract \(x^3\) from both sides which would cancel \(x^3\) and leave you with:
\((2x^2 - 2x^2) + (x - 4x) + 2 = 0\)

Answer 19

Obviously \(2x^2 - 2x^2 = 0\) so what you're really left with is

\(x - 4x + 2 = 0\)

I'm certain you could finish solving that on your own.

Answer 20

yes, but i have one more question about what you did. I can solve from here

Answer 21

so you just multiplied the binomials, is that right??

Answer 22

Yes, exactly

Answer 23

okay!! That makes more sense!!! :D Thanks. I have another problem If i open another post will you help me?

Answer 24

After solving for x, you should check to make sure x still works with the original problem.

Answer 25

Go ahead and post your next post @jessicamccall