Alg3.2.3

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Solve for x\,: x^{-8}-17x^{-4}+16=0\,

Let u=x^{-4}\,

Then u^2-17u+16=0\,

(u-1)(u-16)=0\,

u=1,16\,

There will be a set of solutions for each root.

u=1\,

x^{-4}=1\,

x^4 = \left(x^2\right)^2 = 1\,

x^2 = \pm 1\,

x = \pm 1, \pm i\,

u=16\,

x^{-4}=16\,

x^4 = \left(x^2\right)^2 = \frac{1}{16}\,

x^2 = \pm \frac{1}{4}\,

x = \pm \frac{1}{2}, \pm \frac{1}{2}i\,



The solution is

x=\pm 1, \pm i, \pm \frac{1}{2}, \pm \frac{1}{2}i\,

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