\(a,\)\(R1.R4=R2.R3\Rightarrow\dfrac{R1}{R2}=\dfrac{R3}{R4}\Rightarrow\left(R1ntR3\right)//\left(R2ntR4\right)\)
\(\Rightarrow\left\{{}\begin{matrix}R1.R4=20^2=400\left(\Omega\right)\Rightarrow R1=\dfrac{400}{R4}\left(1\right)\\I13=\dfrac{U}{R13}=\dfrac{18}{R1+R3}=\dfrac{18}{R1+20}\left(A\right)\\I24=\dfrac{18}{R2+R4}=\dfrac{18}{R4+20}\left(A\right)\end{matrix}\right.\)
\(\Rightarrow Im=I13+I24=\dfrac{18}{R1+20}+\dfrac{18}{R4+20}=\dfrac{18}{Rtd}=\dfrac{18}{\dfrac{\left(R1+R3\right)\left(R2+R4\right)}{R1+R2+R3+R4}}=\dfrac{18}{\dfrac{\left(20+R1\right)\left(20+R4\right)}{R1+R4+40}}\left(2\right)\)
\(\left(1\right)\left(2\right)\Rightarrow\dfrac{18}{\dfrac{400}{R4}+20}+\dfrac{18}{R4+20}=\dfrac{18}{\dfrac{\left(\dfrac{400}{R4}+20\right)\left(R4+20\right)}{\dfrac{400}{R4}+R4+40}}\Rightarrow\left\{{}\begin{matrix}R4=5\Omega\\R1=\dfrac{400}{5}=80\Omega\end{matrix}\right.\)
\(\Rightarrow Rtd=\dfrac{\left(R1+R3\right)\left(R2+R4\right)}{R1+R2+R3+R4}=\dfrac{\left(20+80\right)\left(20+5\right)}{20+80+20+5}=20\Omega\)
\(b,\Rightarrow\left(R3//R2\right)nt\left(R1//R4\right)\Rightarrow\)\(Ia=0,3A=I3-I1\)
\(\Rightarrow\dfrac{I4}{I1}=\dfrac{R1}{R4}\Rightarrow I1=\dfrac{R4.I4}{R1}=\dfrac{R4\left(Im-I1\right)}{R1}\left(A\right)\)
\(\Rightarrow Im=\dfrac{18}{Rtd}=\dfrac{18}{\dfrac{R2R3}{R2+R3}+\dfrac{R1R4}{R1+R4}}=\dfrac{18}{10+\dfrac{400}{R1+R4}}\left(A\right)\)
\(\Rightarrow I1=\dfrac{U-U23}{R1}=\dfrac{18-Im.R23}{R1}=\dfrac{18-\dfrac{180}{10+\dfrac{400}{R1+R4}}}{R1}=\dfrac{\dfrac{180+\dfrac{7200}{R1+R4}-180}{10+\dfrac{400}{R1+R4}}}{R1}=\dfrac{\dfrac{\dfrac{7200}{R1+R4}}{\dfrac{10R1+10R4+400}{R1+R4}}}{R1}=\dfrac{\dfrac{7200}{10R1+10R4+400}}{R1}=\dfrac{7200}{R1\left(10R1+10R4+400\right)}=\dfrac{7200}{10R1^2+400R1+4000}\left(A\right)\)
\(\Rightarrow I3+I2=Im\Rightarrow I3=\dfrac{Im}{2}=\dfrac{\dfrac{18}{10+\dfrac{400}{R1+R4}}}{2}=\dfrac{9}{10+\dfrac{400}{R1+R4}}\left(A\right)\)
\(\Rightarrow\dfrac{9}{10+\dfrac{400}{R1+R4}}-\dfrac{7200}{10R1^2+400R1+4000}=0,3\Rightarrow\dfrac{9}{10+\dfrac{400}{R1+\dfrac{400}{R1}}}-\dfrac{7200}{10R1^2+400R1+4000}=0,3\Rightarrow\left\{{}\begin{matrix}R1=40\Omega\\R4=10\Omega\end{matrix}\right.\)\(\)
