An algebra problem by Julian Yu

We have ${ (x+\frac { 1 }{ x } ) }^{ 2 }={ 3 }^{ 2 }$ , so ${ { x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } }+2=9$ , and ${ { x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } }=7$ .

Hence ${ (x-\frac { 1 }{ x } ) }^{ 2 } = { x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } -2 = 7-2 = 5$ , and $\left| x-\frac { 1 }{ x } \right| =\sqrt { 5 } \approx \boxed { 2.236 }$