Resistors

Two resistors connected in series give the resulting resistance 245Ω and 60Ω in parallel. Determine the resistance of these resistors.

Correct answer:

R₁ =  105 Ω
R₂ =  140 Ω

Step-by-step explanation:

$$\begin{gathered} {R}_1+R_2=245\mathrm{\Omega } \\ {\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{R_2}}={\displaystyle \frac{1}{60\mathrm{\Omega }}} \\ {R}_2=245-R_1 \\ {\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{245-R_1}}={\displaystyle \frac{1}{60\mathrm{\Omega }}} \\ {R}_1^2-245R_1+245\cdot 60=0 \\ {R}_1^2-245R_1+14700=0 \\ (R_1-105)\cdot (R_1-140)=0 \\ {R}_1=105\mathrm{\Omega } \\ {R}_2=140\mathrm{\Omega } \end{gathered}$$

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