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Here is my code:

f0[\[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*\[Lambda]0^2)^2 + 4*x^2*(1 - k^2*x)*\[Lambda]0^2*Abs[-(k*y0) + y1 + k*\[Lambda]0^2 - x*\[Lambda]0^2]

f1[\[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(-k + x)*\[Lambda]1^2*Abs[-(k*y0) + y1 - \[Lambda]1^2 + k^2*x*\[Lambda]1^2]

f2[\[Lambda]0_, \[Lambda]1_, x_, k_] :=-1/27 + \[Lambda]0^3 + 3*x*\[Lambda]0^2*\[Lambda]1 + 3*k*x*\[Lambda]0*\[Lambda]1^2 + \[Lambda]1^3

$k$ is some positive number which can be chosen freely for example $k=1$ or $k=3/2$ or $k=2/3$. $f_0$ is only a function of $\lambda_0$, likewise $f_1$ is only a function of $\lambda_1$.

If I would insert $\lambda_0$ from $f_0$ into $f_2$ and insert $\lambda_1$ from $f_1$ into $f_2$ then $f_2$ will be a function of only $x,k,y_0,y_1$.

In this case I would like to have a 3D plot with x axis =$y_0$, y-axis=$y_1$, and z-axis =$x$ for $7/81<y_0<1/9$ and $7/81<y_1<1/9$, for some known $k$ as mentioned above and $x$ must be eventually in $0<x<1$, by positivity condition. Is it doable? how can I do that?

EDIT:

I obtain the polynomials via equating them to $0$. Namely $f_0=0$, $f_1=0$ and $f_2=0$ are all given and known. Thank you very much.

Here is my code:

f0[\[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*\[Lambda]0^2)^2 + 4*x^2*(1 - k^2*x)*\[Lambda]0^2*Abs[-(k*y0) + y1 + k*\[Lambda]0^2 - x*\[Lambda]0^2]

f1[\[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(-k + x)*\[Lambda]1^2*Abs[-(k*y0) + y1 - \[Lambda]1^2 + k^2*x*\[Lambda]1^2]

f2[\[Lambda]0_, \[Lambda]1_, x_, k_] :=-1/27 + \[Lambda]0^3 + 3*x*\[Lambda]0^2*\[Lambda]1 + 3*k*x*\[Lambda]0*\[Lambda]1^2 + \[Lambda]1^3

$k$ is some positive number which can be chosen freely for example $k=1$ or $k=3/2$ or $k=2/3$. $f_0$ is only a function of $\lambda_0$, likewise $f_1$ is only a function of $\lambda_1$.

If I would insert $\lambda_0$ from $f_0$ into $f_2$ and insert $\lambda_1$ from $f_1$ into $f_2$ then $f_2$ will be a function of only $x,k,y_0,y_1$.

In this case I would like to have a 3D plot with x axis =$y_0$, y-axis=$y_1$, and z-axis =$x$ for $7/81<y_0<1/9$ and $7/81<y_1<1/9$, for some known $k$ as mentioned above and $x$ must be eventually in $0<x<1$, by positivity condition. Is it doable? how can I do that?

EDIT:

I obtain the polynomials via equating them to $0$. Namely, $f_0=0$, $f_1=0$ and $f_2=0$ are all given and known.

Thank you very much.

Here is my code:

f0[\[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(1 - k^2*x)*\[Lambda]1^2*Abs[-(k*y0) + y1 + k*\[Lambda]1^2 - x*\[Lambda]1^2]

f1[\[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(-k + x)*\[Lambda]1^2*Abs[-(k*y0) + y1 - \[Lambda]1^2 + k^2*x*\[Lambda]1^2]

f2[\[Lambda]0_, \[Lambda]1_, x_, k_] :=-1/27 + \[Lambda]0^3 + 3*x*\[Lambda]0^2*\[Lambda]1 + 3*k*x*\[Lambda]0*\[Lambda]1^2 + \[Lambda]1^3

$k$ is some positive number which can be chosen freely for example $k=1$ or $k=3/2$ or $k=2/3$. $f_0$ is only a function of $\lambda_0$, likewise $f_1$ is only a function of $\lambda_1$.

If I would insert $\lambda_0$ from $f_0$ into $f_2$ and insert $\lambda_1$ from $f_1$ into $f_2$ then $f_2$ will be a function of only $x,k,y_0,y_1$.

In this case I would like to have a 3D plot with x axis =$y_0$, y-axis=$y_1$, and z-axis =$x$ for $7/81<y_0<1/9$ and $7/81<y_1<1/9$, for some known $k$ as mentioned above and $x$ must be eventually in $0<x<1$, by positivity condition. Is it doable? how can I do that?

EDIT:

I obtain the polynomials via equating them to $0$. Namely $f_0=0$, $f_1=0$ and $f_2=0$ are all given and known. Thank you very much.

Here is my code:

f0[\[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*\[Lambda]0^2)^2 + 4*x^2*(1 - k^2*x)*\[Lambda]0^2*Abs[-(k*y0) + y1 + k*\[Lambda]0^2 - x*\[Lambda]0^2]

f1[\[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(-k + x)*\[Lambda]1^2*Abs[-(k*y0) + y1 - \[Lambda]1^2 + k^2*x*\[Lambda]1^2]

f2[\[Lambda]0_, \[Lambda]1_, x_, k_] :=-1/27 + \[Lambda]0^3 + 3*x*\[Lambda]0^2*\[Lambda]1 + 3*k*x*\[Lambda]0*\[Lambda]1^2 + \[Lambda]1^3

$k$ is some positive number which can be chosen freely for example $k=1$ or $k=3/2$ or $k=2/3$. $f_0$ is only a function of $\lambda_0$, likewise $f_1$ is only a function of $\lambda_1$.

If I would insert $\lambda_0$ from $f_0$ into $f_2$ and insert $\lambda_1$ from $f_1$ into $f_2$ then $f_2$ will be a function of only $x,k,y_0,y_1$.

In this case I would like to have a 3D plot with x axis =$y_0$, y-axis=$y_1$, and z-axis =$x$ for $7/81<y_0<1/9$ and $7/81<y_1<1/9$, for some known $k$ as mentioned above and $x$ must be eventually in $0<x<1$, by positivity condition. Is it doable? how can I do that?

EDIT:

I obtain the polynomials via equating them to $0$. Namely $f_0=0$, $f_1=0$ and $f_2=0$ are all given and known. Thank you very much.

Here is my code:

f0[\[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(1 - k^2*x)*\[Lambda]1^2*Abs[-(k*y0) + y1 + k*\[Lambda]1^2 - x*\[Lambda]1^2]

f1[\[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(-k + x)*\[Lambda]1^2*Abs[-(k*y0) + y1 - \[Lambda]1^2 + k^2*x*\[Lambda]1^2]

f2[\[Lambda]0_, \[Lambda]1_, x_, k_] :=-1/27 + \[Lambda]0^3 + 3*x*\[Lambda]0^2*\[Lambda]1 + 3*k*x*\[Lambda]0*\[Lambda]1^2 + \[Lambda]1^3

$k$ is some positive number which can be chosen freely for example $k=1$ or $k=3/2$ or $k=2/3$. $f_0$ is only a function of $\lambda_0$, likewise $f_1$ is only a function of $\lambda_1$.

If I would insert $\lambda_0$ from $f_0$ into $f_2$ and insert $\lambda_1$ from $f_1$ into $f_2$ then $f_2$ will be a function of only $x,k,y_0,y_1$.

In this case I would like to have a 3D plot with x axis =$y_0$, y-axis=$y_1$, and z-axis =$x$ for $7/81<y_0<1/9$ and $7/81<y_1<1/9$, for some known $k$ as mentioned above and $x$ must be eventually in $0<x<1$, by positivity condition. Is it doable? how can I do that?

EDIT: I obtain the polynomials via equating them to $0$. Namely $f_0=0$, $f_1=0$ and $f_2=0$ are all given and known. Thank you very much.

Here is my code:

f0[\[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(1 - k^2*x)*\[Lambda]1^2*Abs[-(k*y0) + y1 + k*\[Lambda]1^2 - x*\[Lambda]1^2]

f1[\[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*\[Lambda]1^2)^2 + 4*x^2*(-k + x)*\[Lambda]1^2*Abs[-(k*y0) + y1 - \[Lambda]1^2 + k^2*x*\[Lambda]1^2]

f2[\[Lambda]0_, \[Lambda]1_, x_, k_] :=-1/27 + \[Lambda]0^3 + 3*x*\[Lambda]0^2*\[Lambda]1 + 3*k*x*\[Lambda]0*\[Lambda]1^2 + \[Lambda]1^3

$k$ is some positive number which can be chosen freely for example $k=1$ or $k=3/2$ or $k=2/3$. $f_0$ is only a function of $\lambda_0$, likewise $f_1$ is only a function of $\lambda_1$.

If I would insert $\lambda_0$ from $f_0$ into $f_2$ and insert $\lambda_1$ from $f_1$ into $f_2$ then $f_2$ will be a function of only $x,k,y_0,y_1$.

In this case I would like to have a 3D plot with x axis =$y_0$, y-axis=$y_1$, and z-axis =$x$ for $7/81<y_0<1/9$ and $7/81<y_1<1/9$, for some known $k$ as mentioned above and $x$ must be eventually in $0<x<1$, by positivity condition. Is it doable? how can I do that?

EDIT: 

I obtain the polynomials via equating them to $0$. Namely $f_0=0$, $f_1=0$ and $f_2=0$ are all given and known. Thank you very much.