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# Difficult cubic equation. Watch

1. By using a substitution to remove the term in , or otherwise, find the single real solution to the equation
.
2. how far have you got ?
3. (Original post by the bear)
how far have you got ?
Used substitution to get it down to .
4. this should help:

*
5. (Original post by Ano123)
Used substitution to get it down to .
Remember cos 3x = 4 cos^3x - 3cosx
6. (Original post by Mathemagicien)
Remember cos 3x = 4 cos^3x - 3cosx
I'm not sure if that helps here.
I'd get if I just did it like that.
7. (Original post by Ano123)
I'm not sure if that helps here.
I'd get if I just did it like that.
So use cos

so

which is a quadratic in

which gives you

take logs, we get

and you can find cos (and thus y and thus x) from that

so

(which satisfies our equation)
8. (Original post by Mathemagicien)
So

which is a quadratic in

which gives you

take logs, we get

and you can find cos from that

I get cos
Not very nice looking solutions though are they? What have you done to get from there?
Oh, I see.
9. (Original post by Ano123)
Not very nice looking solutions though are they? What have you done to get from there?
Compared to this...

(Original post by the bear)
this should help:
*
10. (Original post by Mathemagicien)
So use cos

so

which is a quadratic in

which gives you

take logs, we get

and you can find cos (and thus y and thus x) from that

I get cos (which satisfies our equation)
What does the mean?
11. (Original post by Ano123)
What does the mean?
Plus or minus (don't know the latex for it)
12. (Original post by Mathemagicien)
Plus or minus (don't know the latex for it)
\pm
13. (Original post by Mathemagicien)
Plus or minus (don't know the latex for it)
Thought so. \pm - code for it.
I'll tell you I have got the solution to this equation but I used . It's slightly easier doing this but I actually like your method a lot. Thanks!
14. (Original post by Ano123)
Thought so. \pm - code for it.
I'll tell you I have got the solution to this equation but I used . It's slightly easier doing this but I actually like your method a lot. Thanks!
You could also use y=cosh t, cosh 3t = 4 cosh^3 t - 3 cosh t, its equivalent
15. (Original post by Mathemagicien)
You could also use y=cosh t, cosh 3t = 4 cosh^3 t - 3 cosh t, its equivalent
That's what I meant I used cosh not sinh.
16. Exams are over. Chill the **** out.
17. (Original post by Randall13)
Exams are over. Chill the **** out.
Why?
18. (Original post by Randall13)
Exams are over. Chill the **** out.
this!
19. (Original post by Randall13)
Exams are over. Chill the **** out.
I don't do this for exams. Exams are over and I'm bored so may as well do some more maths, what could I be doing that's more interesting than that?

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