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!

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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)   (Show Source): You can put this solution on YOUR website!
{xy = 20
2x^2 - y^2 + 4 = 0
---------------
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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=804 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 13.1774468787578, -15.1774468787578. Here's your graph:

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

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