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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let z=x%5E2+-3. So this means that z%5E2=%28x%5E2+-3%29%5E2


So the equation %28x%5E2+-3%29%5E2+%2B+%28x%5E2+-3%29+-2=0 simplifies to z%5E2%2Bz-2=0




z%5E2%2Bz-2=0 Start with the given equation.


Notice we have a quadratic equation in the form of az%5E2%2Bbz%2Bc where a=1, b=1, and c=-2


Let's use the quadratic formula to solve for z


z+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


z+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-2


z+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


z+=+%28-1+%2B-+sqrt%28+1--8+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-2%29 to get -8


z+=+%28-1+%2B-+sqrt%28+1%2B8+%29%29%2F%282%281%29%29 Rewrite sqrt%281--8%29 as sqrt%281%2B8%29


z+=+%28-1+%2B-+sqrt%28+9+%29%29%2F%282%281%29%29 Add 1 to 8 to get 9


z+=+%28-1+%2B-+sqrt%28+9+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


z+=+%28-1+%2B-+3%29%2F%282%29 Take the square root of 9 to get 3.


z+=+%28-1+%2B+3%29%2F%282%29 or z+=+%28-1+-+3%29%2F%282%29 Break up the expression.


z+=+%282%29%2F%282%29 or z+=++%28-4%29%2F%282%29 Combine like terms.


z+=+1 or z+=+-2 Simplify.


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Now remember, we let z=x%5E2-3.


z+=+1 Go back to the first equation


x%5E2-3+=+1 Plug in z=x%5E2-3


x%5E2=1%2B3Add 3 to both sides.


x%5E2=4 Combine like terms.


x=0%2B-sqrt%284%29 Take the square root of both sides.


x=sqrt%284%29 or x=-sqrt%284%29 Break up the "plus/minus" to form two equations.


x=2 or x=-2 Take the square root of 4 to get 2.



So the first two solutions are x=2 or x=-2.


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z+=+-2 Now move onto the second equation


x%5E2-3+=+-2 Plug in z=x%5E2-3


x%5E2=-2%2B3Add 3 to both sides.


x%5E2=1 Combine like terms.


x=0%2B-sqrt%281%29 Take the square root of both sides.


x=sqrt%281%29 or x=-sqrt%281%29 Break up the "plus/minus" to form two equations.


x=1 or x=-1 Take the square root of 1 to get 1.



So the next two solutions are x=1 or x=-1.


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Answer:


So the solutions are

x=2, x=-2, x=1 or x=-1


Note: the order of the solutions does not matter.

Answer by scott8148(6628) About Me  (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