Find the y-coordinates for the point of intersection of the curve y = x2 with the circle x2 + y2 = 1

I have halfway used simultaneous equations and I have the equation:
x2 + x4 = 1
How do I solve for x?

Let x^2=z

z^2+z=1

z^2+z-1=0

Using the quadratic formula yields z=\frac{-1+\sqrt 5}{2} or z=\frac{-1-\sqrt 5 }{2}

Since only the left expression is nonnegative, we only take the square root of that.

x=\sqrt z
x=\sqrt \frac{-1+\sqrt 5}{2}

=\pm 0.786

After graphing both equations on Desmos, my solution appears to be correct.

You can treat this as a hidden quadratic.
x4+x2-1=0
let a=x2
a2+a-1=0 --> Solve using quadratic formula
a=-1+/-sqrt(12-4(a)(-1))/2(1)
a=-1+/-sqrt(5)/2

Then square root the a value to find x. Let me know if you need more clarification 🙂

Ohhh ok.
so you move the 1 over and treat it as a quadratic and solve using the quadratic formula.
So if you were finding x from the x2 part there is a +/- in front of the sqrt of a, but there is also a +/- in front of the sqrt(5) doesn't that mean there will be four answers??

    Remember that you cannot square root a negative number in Methods.

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