Two known resistance of $R\Omega$ and $2R\Omega$ and and one unknown resistance $X\Omega$ are connec

Question

Two known resistance of $R\Omega$ and $2R\Omega$ and and one unknown resistance $X\Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $X\Omega$, then the value of X is $\_\_\_\_$ $\Omega$.

Accepted Answer

$\frac{(2R + x) \cdot (R)}{3R + x} = x$$${x^{2} + 2Rx - 2R^{2} = 0 }{x = (\sqrt{3} - 1)R}$$

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