A planet, a comet, and an asteroid have orbits around the same star.

The position of the comet and the asteroid can be determined by their distance, x, from the star and their angle, from the planet-star axis.

Physicists know the path of the comet, x() = ³ and the path of the asteroid, x() = 7, intersect.

We wish to help the Physicists estimate the -value at which the two curves intersect using

Newton's Method.

Let ₀ = 2. Compute the first two iterations of Newton's method, ₁ and ₂

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_{Thank you!}