Harry23 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?
WelcomeToHell 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
ArtyDReams 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 🙂
Harry23 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??
