Two resistors are connected $(a)$ in series $(b)$ in parallel. The equivalent resistance in the two cases are $9$ $ohm$ and $2$ $ohm$ respectively. Then the resistances of the component resistors are
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(b) ${R_1} + {R_2} = 9$ and $\frac{{{R_1}{R_2}}}{{{R_1} + {R_2}}} = 2$ $ \Rightarrow $ ${R_1}{R_2} = 18$
${R_1} - {R_2} = \sqrt {{{({R_1} + {R_2})}^2} - 4{R_1}{R_2}} = \sqrt {81 - 72} = 3$
${R_1} = 6\,\Omega ,\,{R_2} = 3\,\Omega $
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