Given `f(x+1/x)=x^2+1/x^2` find `f(x)` :

We try `f(x)=x^2` and we get `f(x+1/x)=(x+1/x)^2=x^2+2+1/x^2`

This is close. We realize we need to subtract 2 so:

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`f(x)=x^2-2`

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Check: `f(x+1/x)=(x+1/x)^2-2=x^2+2+1/x^2-2=x^2+1/x^2` as required.