SOLUTION: I have tryed these four questions a few times each and have come up with dif answers each time!! I know that I am missing something and was wondering if you could help!! These ar

Question 170212: I have tryed these four questions a few times each and have come up with dif answers each time!! I know that I am missing something and was wondering if you could help!! These are practice questions for an upcoming exam! I have to be able to get consistant answers!! Please help if you can!! Thank you..
(x^2 -3)^2 + (x^2 -3) -2=0
"^" indicates "squared"

Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let . So this means that

So the equation simplifies to

Start with the given equation.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for z

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

----------------------------------------------------------------

Now remember, we let .

Go back to the first equation

Plug in

Add to both sides.

Combine like terms.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Take the square root of to get .

So the first two solutions are or .

----------------------------------------------------------

Now move onto the second equation

Plug in

Add to both sides.

Combine like terms.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Take the square root of to get .

So the next two solutions are or .

=========================================================================

Answer:

So the solutions are

, , or

Note: the order of the solutions does not matter.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this is a quadratic equation with (x^2 -3) as the variable

imagine if (x^2 -3) is m, then m^2 + m - 2 = 0, which factors to (m+2)(m-1)=0

factoring __ [(x^2 -3)+2][(x^2 -3)-1]=0

x^2 -3 +2 = 0 __ x^2 -1 = 0 __ factoring __ (x+1)(x-1)=0 __ x=1, x=-1

x^2 -3 -1 = 0 __ x^2 -4 = 0 __ factoring __ (x+2)(x-2)=0 __ x=2, x=-2
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