x^2+1/(x^2)=1

解

x^{2} + \frac{1}{x ^{2}} = 1

x = \frac{3}{2} + \frac{1}{2} i, x = - \frac{3}{2} - \frac{1}{2} i, x = \frac{3}{2} - \frac{1}{2} i, x = - \frac{3}{2} + \frac{1}{2} i

解答ステップ

x^{2} + \frac{1}{x ^{2}} = 1

以下で両辺を乗じる:

x^{2}

x^{4} + 1 = x^{2}

解く

x^{4} + 1 = x^{2} : x = \frac{3}{2} + \frac{1}{2} i, x = - \frac{3}{2} - \frac{1}{2} i, x = \frac{3}{2} - \frac{1}{2} i, x = - \frac{3}{2} + \frac{1}{2} i

x = \frac{3}{2} + \frac{1}{2} i, x = - \frac{3}{2} - \frac{1}{2} i, x = \frac{3}{2} - \frac{1}{2} i, x = - \frac{3}{2} + \frac{1}{2} i