Math Is Fun Forum

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Solve in R..

(A, B, C) € R
A + B + C = 5
AB + BC + CA = 0
ABC = -11
How to find A, B, C?

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If two or more thoughts intersect, there has to be a point!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Solve in R..

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Solve in R..

mmm... actually what i real was trying to do was the same thing!
Means..
I was trying to solve the cubic equation x^3+5x-11=0.
I wrote x^3+5x-11=(x-a)(x-b)(x-c)=0
upon equating the coefficients i get the above system of equations which i really can't solve...
Any suggestions or ways?

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If two or more thoughts intersect, there has to be a point!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Solve in R..

I’m afraid that cubic equation doesn’t have nice solutions. But you can still solve it in closed form, e.g. by Cardano’s method. Trouble is, the working may be very very tedious, and the answers may be totally horrible-looking.