# Join the resistance!

In a circuit we have three resistances, ${ R }_{ 1 }$, ${ R }_{ 2 }$ and ${ R }_{ 3 }$. It's known that ${ R }_{ 1 }=a$, ${ R }_{ 2 }={ a }^{ 2 }$ and ${ R }_{ 3 }={ a }^{ 3 }$. Also we know that if we create a parallel circuit with ${ R }_{ 1 }$, ${ R }_{ 2 }$ and ${ R }_{ 3 }$ the total resistance is ${ R }_{ p }$ but if we create a series circuit with them, the total resistance is ${ R }_{ s }$. If $9{ R }_{ p }={ R }_{ s }$, calculate the value of ${ R }_{ 1 }$.

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