x^3+(27)/(x^3)=28

解

x^{3} + \frac{27}{x ^{3}} = 28

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

解答ステップ

x^{3} + \frac{27}{x ^{3}} = 28

以下で両辺を乗じる:

x^{3}

x^{6} + 27 = 28 x^{3}

解く

x^{6} + 27 = 28 x^{3} : x = 3, x = - \frac{3}{2} + \frac{3 3}{2} i, x = - \frac{3}{2} - \frac{3 3}{2} i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

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

解を検算する

未定義の (特異) 点を求める:

x = 0

未定義のポイントを解に組み合わせる:

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