SOLUTION: {{{Find the points (if any) where the circle x^2 + y^2 = 50 intersects the parabola y=x^2-1. Give exact answers. Do not approximate irrational numbers with decimals.}}} I am ab

Question 969308: I am able to get a sketch of the graph, but answer comes up in decimals and not exact answers. I am getting points :
(-2.741867, 6.51783441), (2.741867, 6.51783441) Am I close or way off?
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Substitute,

So,

Then you can calculate x,

Yes, that's it.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the points (if any) where the circle x^2 + y^2 = 50 intersects the parabola y=x^2-1
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Sub for y in the circle's equation.
x^2 + (x^2-1)^2 = 50

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=197 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.5178344238091, -6.5178344238091. Here's your graph:

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real number
real number
complex number
complex number
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Find y using
for both real number solutions.

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