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How to Invert functions with same input variables?

Dear Sirs, I want to invert following set of equations:

Y(i)=a(i)X1+b(i)X2+c(i)X3+d(i)X1X2+e(i)X1X3+f(i)X2X3+g(i)X1^2+h(i)X2^2+i(i)X3^2 i=[1,4]

It consists of four outputs (Y1-Y4), 3 inputs (X1-X3), and (9*4) coeff.

I intend to generate X1,X2,X3=function(Y1,Y2,Y3,Y4).i.e. Equations of X1,X2,X3. We may assume coefficients of your choice to simplify the solution. Please help me with possible guidance.

POSTED BY: Ajay Goyal
POSTED BY: Gianluca Gorni
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