For Example, I have the following polynomial equations:
$$ \left\{ \begin{array}{ll} \dfrac{2025 (208 x+5 (y-3446))}{52 (y+90)^2}+\dfrac{300 (8 x-21 y+1920) (y-80)}{7 (x+30)^3}+\frac{300 (80 x-21 z+4500) (z-100)}{7 (x+30)^3}-\dfrac{1521 (-539 x+50 z+15425)}{539 (z+39)^2} =0\\[30pt] \frac{2025 (445 y-208 z+49410) (z-45)}{52 (y+90)^3}-\dfrac{2025 (x-85) (208 x+5 (y-3446))}{52 (y+90)^3}-\frac{300 (8 x-21 y+1920)}{7 (x+30)^2}-\frac{1521 (-539 y+90 z+19680)}{539 (z+39)^2} =0\\[30pt] \frac{2025 (445 y-208 z+49410)}{52 (y+90)^2}+\frac{300 (80 x-21 z+4500)}{7 (x+30)^2}+\frac{1521 (x-25) (539 x-25 (2 z+617))}{539 (z+39)^3}+\frac{1521 (y-30) (539 y-30 (3 z+656))}{539 (z+39)^3}=0 \\ \end{array} \right.$$
The mathematica expression:
{{(300 (1920 + 8 x - 21 y) (-80 + y))/(7 (30 + x)^3) + (
2025 (208 x + 5 (-3446 + y)))/(52 (90 + y)^2) + (
300 (4500 + 80 x - 21 z) (-100 + z))/(7 (30 + x)^3) - (
1521 (15425 - 539 x + 50 z))/(
539 (39 + z)^2)}, {-((300 (1920 + 8 x - 21 y))/(7 (30 + x)^2)) - (
2025 (-85 + x) (208 x + 5 (-3446 + y)))/(52 (90 + y)^3) + (
2025 (49410 + 445 y - 208 z) (-45 + z))/(52 (90 + y)^3) - (
1521 (19680 - 539 y + 90 z))/(
539 (39 + z)^2)}, {-((2025 (49410 + 445 y - 208 z))/(
52 (90 + y)^2)) - (300 (4500 + 80 x - 21 z))/(7 (30 + x)^2) - (
1521 (-25 + x) (539 x - 25 (617 + 2 z)))/(539 (39 + z)^3) - (
1521 (-30 + y) (539 y - 30 (656 + 3 z)))/(539 (39 + z)^3)}}
How to extract only those real solutions as new Rule? I mean a general approach to such solutions with mixed real and complex solutions in a rule.
Solve
,Reduce
,NSolve
you can specify a domain for your unknowns,Reals
in your case. $\endgroup$