Question 474250
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Let *[tex \Large u\ =\ x^2]


Then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6u^2\ -\ 11u\ +\ 3\ =\ 0]


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2u\ -\ 3)(3u\ -\ 1)]


Hence *[tex \Large u\ =\ \frac{3}{2}] or *[tex \Large u\ =\ \frac{1}{3}]


But *[tex \Large u\ =\ x^2]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \pm\frac{\sqrt{6}}{2}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \pm\frac{\sqrt{3}}{3}]


Presuming you understand rationalizing denominators.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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