# Simplfying function

#### alexgo

where do I start by making this equal r. I have been trying for an hour. Can't figure it out. I don't need the exact answer. Just the simplfied answer.

$$\displaystyle 0=200 pi r+400 pi-2/r-200/( pi r^3)$$

#### Anonymous1

where do I start by making this equal r. I have been trying for an hour. Can't figure it out. I don't need the exact answer. Just the simplfied answer.

$$\displaystyle 0=200 pi r+400 pi-2/r-200/( pi r^3)$$
$$\displaystyle 0=200 \pi r+400 \pi-\frac{2}{r}-\frac{200}{ \pi r^3}$$

$$\displaystyle 0=\frac{200 \pi^2 r^4 + 400 \pi^2 r^3 - 2\pi r^2 -200}{ \pi r^3}$$

So the whole thing =0 when the numerator =0,

$$\displaystyle 200 \pi^2 r^4 + 400 \pi^2 r^3 - 2\pi r^2 -200 = 0$$

...Which can be done by factoring and inspection, a computer, or long division.

Last edited:
alexgo