I'm trying to solve the following system of equations in $R$ and $m$ for fixed $k>0$ and $l\in\mathbb{R}$: $$ \left\{ \begin{aligned} k&=\frac{R}{m^2+R^2}, \\ l&=\frac{m}{m^2+R^2} \end{aligned} \right.. $$ Is there a method to solve this system of equations? I tried rewriting the first equation to a quadratic one in the variable $R$ in order to use the quadratic formula. But that didn't really get me any closer to the solution, I think.
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3Yes, you can multiply by $m^2+R^2$ to obtain two polynomial equations. Using the resultant you can solve it. If you want, I can write out the solution. More easily, multiply the first equation by $l$ and the second by $k$. This yields $km=lR$. Then substitute $m=\frac{l}{k}R$. – Dietrich Burde Dec 26 '23 at 19:20
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Welcome to Math SE. FYI, using an Approach0 search, there's the quite similar Find the value of $x +y$, where its answers provide several approaches you can use. – John Omielan Dec 26 '23 at 19:25
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Does this answer your question? Find the value of $x +y$ – Integrand Jan 01 '24 at 16:53
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Note that one has $ml+Rk=1$ and $mk=lR$ from the two given expressions. Now one can solve the system of simultaneous equations.
ShyamalSayak
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