Inspired by Victor Paes Plinio

Calculus Level 4

$\frac{x}{2}+\frac{x^{4}}{8}+\frac{x^{7}}{32}+\frac{x^{10}}{128}+\ldots = 18$

find the product of all possible $x$ .

36 4 -4 -36

1 solution

Li Yuelin
May 11, 2015

If we multiply the equation by $x^{3}$ and divide it by $4$ , we get $\frac{x}{2}$ less than the original equation, so

$\frac{18x^3}{4} = 18-\frac{x}{2}$

Simplifying, we get $9x^{3} = 36-x \longrightarrow 9x^{3}+x-36 = 0$ .

With Vieta's Formula, we have product of roots $= \boxed{4}$ .

I changed your solution into LaTeX! If you would like to learn LaTeX or just write a solution, I recommend the useful formatting guide, or other guides on the site! Happy solving.

Jake Lai - 6 years, 1 month ago

Thanks! I had been wondering about what people are using to write these stuff for a long time, and now I finally know it.

Li Yuelin - 6 years, 1 month ago

I am sorry

just

need to know how this works

$sin\ (3^{2} \times 10)^\circ = \boxed{1}$

Yes
I
Made
It

Li Yuelin - 6 years, 1 month ago

You could have used GP

Department 8 - 5 years, 6 months ago

we need |x|<1. can you prove all roots satisfy this?

Aareyan Manzoor - 5 years, 6 months ago

At some points in time, I tried to: - Differentiate the function that determines each part of the progression ; - Attempt solving cubic equation

Li Yuelin - 6 years, 1 month ago

Inspired by Victor Paes Plinio

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