Example

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

Question

$${ M }^{ 2 } -1/M=6FINDTHEVALUEOF { M }^{ 2 } +1/ { M }^{ 2 } ANDM+1/ { M }^{ 2 }$$

Answer

M=-0.72449188232422,1.220743560791

Solution


Simplify  \(\frac{1}{{M}^{2}}ANDM\)  to  \(\frac{ANDM}{{M}^{2}}\).
\[{M}^{2}-\frac{1}{M}=6{FINDTHEVALUEOFM}^{2}+\frac{ANDM}{{M}^{2}}+\frac{1}{{M}^{2}}\]
Multiply both sides by the Least Common Denominator: \({M}^{2}\).
\[{M}^{4}-M=6{FINDTHEVALUEOFM}^{2}{M}^{2}+ANDM+1\]
Move all terms to one side.
\[{M}^{4}-M-6{FINDTHEVALUEOFM}^{2}{M}^{2}-ANDM-1=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[M=-0.724492,1.220744\]
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