Question 325936
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10x^4\ -\ 17x^2\ +\ 3\ =\ 0]



Let *[tex \Large u\ =\ x^2], then



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10u^2\ -\ 17u\ +\ 3\ =\ 0]


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (5u\ -\ 1)(2u\ -\ 3)\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u\ =\ \frac{1}{5}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u\ =\ \frac{3}{2}]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ \frac{1}{5}\ \Rightarrow\ x\ =\ \pm\frac{\sqrt{5}}{5}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ \frac{3}{2}\ \Rightarrow\ x\ =\ \pm\frac{\sqrt{6}}{2}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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