Question 689024
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Let *[tex \LARGE u\ =\ (m\ +\ 5)^2]


Then *[tex \LARGE (m\ +\ 5)^4\ -\ 4(m\ +\ 5)^2\ +\ 4\ =\ 0]


Can be written *[tex \LARGE u^2\ -\ 4u\ +\ 4\ =\ 0]


Solve for *[tex \LARGE u]


*[tex \LARGE (u\ -\ 2)^2\ =\ 0]


So *[tex \LARGE u\ =\ 2] or *[tex \LARGE u\ =\ 2]


But *[tex \LARGE u\ =\ (m\ +\ 5)^2]


*[tex \LARGE m\ +\ 5\ =\ \pm\sqrt{2}]


*[tex \LARGE m\ =\ -5\ \pm\sqrt{2}]


There are two roots, each with a multiplicity of 2 for a total of 4 roots as expected from a 4th degree polynomial equation.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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