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Question Number 56553 by problem solverd last updated on 18/Mar/19

$$\mathrm{solve}\mathrm{for}m$$$$m^8=3125$$

Answered by MJS last updated on 18/Mar/19

$$x^8=a$$$$\mathrm{has}\mathrm{got}8\mathrm{solutions}$$$$x_{1,2}=\pm \sqrt[8]{a}$$$$x_{3,4}=\pm \sqrt[8]{a}\mathrm{i}$$$$x_{5,6,7,8}=\pm \sqrt[8]{a}(\frac{\sqrt{2}}{2}\pm \frac{\sqrt{2}}{2}\mathrm{i})$$$$\mathrm{in}\mathrm{this}\mathrm{case}$$$$m_{1,2}=\pm 5^{5/8}\approx \pm 2.7344$$$$m_{3,4}=\pm 5^{5/8}\mathrm{i}\approx \pm 2.7344\mathrm{i}$$$$m_{5,6,7,8}=\pm 5^{5/8}(\frac{\sqrt{2}}{2}\pm \frac{\sqrt{2}}{2}\mathrm{i})\approx \pm 1.9335\pm 1.9335\mathrm{i}$$

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