Not really sure how to approach this one analytically, any clues?

x^{3}+2x = 5cos x

Cheers,

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- May 1st 2013, 10:46 PMdeSitterIntersection of a circular function and a cubic
Not really sure how to approach this one analytically, any clues?

x^{3}+2x = 5cos x

Cheers, - May 1st 2013, 10:51 PMMarkFLRe: Intersection of a circular function and a cubic
You cannot solve for $\displaystyle x$ explicitly, you will need to use a numeric root finding technique, such as Newton's method to approximate the root. This is a method from differential calculus.

- May 1st 2013, 11:34 PMdeSitterRe: Intersection of a circular function and a cubic
Oh I see, well I'm not familiar with such a technique so I guess a graphical solution will have to suffice. Thank you Mark!

- May 1st 2013, 11:57 PMMarkFLRe: Intersection of a circular function and a cubic
You should find $\displaystyle x\approx0.96707029542400250809$. This is what the computer returns, using a numeric method.