Example

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

Question

$$\frac{ { x }^{ 3 } +5 }{ { x }^{ 2 } } =x(2x-1)$$

Answer

x=-1.0656776428223,1.604842376709

Solution


Simplify  \(\frac{{x}^{3}+5}{{x}^{2}}\)  to  \(x+\frac{5}{{x}^{2}}\).
\[x+\frac{5}{{x}^{2}}=x(2x-1)\]
Multiply both sides by \({x}^{2}\).
\[{x}^{3}+5={x}^{3}(2x-1)\]
Simplify.
\[{x}^{3}+5=2{x}^{4}-{x}^{3}\]
Move all terms to one side.
\[{x}^{3}+5-2{x}^{4}+{x}^{3}=0\]
Simplify  \({x}^{3}+5-2{x}^{4}+{x}^{3}\)  to  \(2{x}^{3}+5-2{x}^{4}\).
\[2{x}^{3}+5-2{x}^{4}=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=-1.065678,1.604842\]
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