SOLUTION: Hi! Find all solutions of the system of equations. (Round each answer to two decimal places. Enter NONE in any unused answer blanks.) {xy = 20 2x^2 - y^2 + 4 = 0 thanks!

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Hi! Find all solutions of the system of equations. (Round each answer to two decimal places. Enter NONE in any unused answer blanks.) {xy = 20 2x^2 - y^2 + 4 = 0 thanks!      Log On


   

Question 200165: Hi!
Find all solutions of the system of equations. (Round each answer to two decimal places. Enter NONE in any unused answer blanks.)
{xy = 20
2x^2 - y^2 + 4 = 0
thanks!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
{xy = 20
2x^2 - y^2 + 4 = 0
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y = 20/x
2x^2 - 400/x^2 + 4 = 0
x^4 + 2x^2 -200 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-200+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-200=804.

Discriminant d=804 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+804+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+804+%29%29%2F2%5C1+=+13.1774468787578
x%5B2%5D+=+%28-%282%29-sqrt%28+804+%29%29%2F2%5C1+=+-15.1774468787578

Quadratic expression 1x%5E2%2B2x%2B-200 can be factored:
1x%5E2%2B2x%2B-200+=+%28x-13.1774468787578%29%2A%28x--15.1774468787578%29
Again, the answer is: 13.1774468787578, -15.1774468787578. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-200+%29

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x^2 = -1 ± sqrt(201)
For the real number solutions:
x^2 = ~ 13.17745
x = ± 3.63
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Complex solutions:
x = ± sqrt(-15.17745)
x = ± 3.90i