Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$${ x }^{ 2 } + \frac{ 1 }{ { x }^{ 2 } } =83$$

Answer

x=-9.1097724914551,-0.10977249145508,0.10977249145508,9.1097724914551

Solution


Multiply both sides by \({x}^{2}\).
\[{x}^{4}+1=83{x}^{2}\]
Move all terms to one side.
\[{x}^{4}+1-83{x}^{2}=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=\pm 9.109772,\pm 0.109772\]
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