I am trying to rearrange 5 equations in terms of 5 variables. I have the equations for y1
, y2
, y3
, y4
and y5
in terms of x1
, x2
, x3
, x4
and x5
, but I want to solve for x1
, x2
, x3
, x4
and x5
in terms of y1
, y2
, y3
, y4
and y5
. I tried the following:
Solve[{y1 == x4*((x2*x3 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y2 == x4*((x1*x3 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y3 == x4*((x1*x2 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y4 == x4*(1/(2*x5 + x2 + x3)),
y5 == x4*(1/(2*x5 + x1 + x3))}, {x1, x2, x3, x4, x5}]
and the output
{}
I looked at this post and thought that maybe I should be using Reduce
, so I tried the following:
Reduce[{y1 == x4*((x2*x3 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y2 == x4*((x1*x3 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y3 == x4*((x1*x2 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y4 == x4*(1/(2*x5 + x2 + x3)),
y5 == x4*(1/(2*x5 + x1 + x3))}, {x1, x2, x3, x4, x5}]
as well as this:
Reduce[{y1 == x4*((x2*x3 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y2 == x4*((x1*x3 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y3 == x4*((x1*x2 - x5^2)/(x1*x2*x3 - (x5^2)*(x1 + x2 + x3) - 2*x5^3)),
y4 == x4*(1/(2*x5 + x2 + x3)),
y5 == x4*(1/(2*x5 + x1 + x3)),
y1 > 0, y2 > 0, y3 > 0, y4 > 0, y5 > 0}, {x1, x2, x3, x4, x5}]
and Mathematica just gets stuck calculating for a long time and doesn't display anything. Is this the correct way to solve this problem? Any suggestions?
x4
is just a scale factor for they
s $\endgroup$Solve
will automatically enforce that denominators do not vanish. In effect it does what you did explicitly. And it turns out that no solutions exist. $\endgroup$