Solving cubic equations using cos(3Θ) identity

[mynamesmurph]

Greetings, I'm stuck and could using a little help.

< link to objectionable page removed >

Here's a picture of the problem. It should be easier than typing it out. I have two questions. Here is the first. I followed along with the example with only one minor problem. Notice how the solutions are x=cos20, cos140, and cos260. Why did they choose cos260 instead of cos 100?

My second question is this. In part a (and b, c, and d for that matter) the cubic equation does not have a ratio of 4:3 like the example problem, (and the identity). How can I get the equation in the proper form?

Thanks

 

[Deleted member 4993]

Greetings, I'm stuck and could using a little help.

< link to objectionable page removed >

Here's a picture of the problem. It should be easier than typing it out. I have two questions. Here is the first. I followed along with the example with only one minor problem. Notice how the solutions are x=cos20, cos140, and cos260. Why did they choose cos260 instead of cos 100?

My second question is this. In part a (and b, c, and d for that matter) the cubic equation does not have a ratio of 4:3 like the example problem, (and the identity). How can I get the equation in the proper form?

Thanks

I cannot read it - not enough resolution to expand.

 

[mynamesmurph]

Try clicking the url, it's a direct link to the image. (I'm not sure why there is an attachment. Do img links automatically become attached like that?)

 

[mynamesmurph]

The link works right?

 

[mynamesmurph]

I think I figured it out, thanks.