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solve equations help.

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xhmv

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Hi folks,

I have 3 equations

xyz=a
x+y+z=b
xy+xz+yz=c

how could I find out x, y, z in terms of a, b and c? I don't have Matlab symbolic math at hands.

Merci.

Could anyone help me and tell me the results?
 

Hi,

your non-linear system can be solved quite easily by pen and paper.

multiply the second equation by x:

x^2 + x*y + x*z=b*x

but from the last one:

x*y+x*z = c - y*z

then:

x^2 + c - y*z = b*x

now, from the first equation:

y*z = a/x

then

x^2 + c - a/x = b*x

or, multiplying by x and rearranging:

x^3 - b*x^2 + c*x - a = 0 (for x <> 0)

solve it using the algorithm for the third degrees equation. Since the system is fully symmetrical, the three solution (if they exist) of the equation will be x, y and z
 

find the roots of x^3-bx^2+cx-a=0
Plot the above equation using any plotting tool, it will intersect the x axis at the values of x,y,z
 

use Maxima!!!!
It is very easy to use~
 

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