Example

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

Question

$${ x }^{ 2 } + \frac{ 1 }{ { x }^{ 2 } } =81$$

Answer

x=-8.9993141174316,-0.1111198425293,0.1111198425293,8.9993141174316

Solution


Multiply both sides by \({x}^{2}\).
\[{x}^{4}+1=81{x}^{2}\]
Move all terms to one side.
\[{x}^{4}+1-81{x}^{2}=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=\pm 8.999314,\pm 0.111120\]
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