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受欢迎的代数 >

x^{-6}-3x^{-3}-28=0

解答

x^{- 6} - 3 x^{- 3} - 28 = 0

解答

x = - \frac{1}{3 4}, x = \frac{1}{2 3 4} - \frac{3}{2 3 4} i, x = \frac{1}{2 3 4} + \frac{3}{2 3 4} i, x = \frac{1}{3 7}, x = - \frac{1}{2 3 7} + \frac{3}{2 3 7} i, x = - \frac{1}{2 3 7} - \frac{3}{2 3 7} i

求解步骤

x^{- 6} - 3 x^{- 3} - 28 = 0

整理后得

\frac{1}{x ^{6}} - \frac{3}{x ^{3}} - 28 = 0

乘以最小公倍数

1 - 3 x^{3} - 28 x^{6} = 0

解

1 - 3 x^{3} - 28 x^{6} = 0 : x = - \frac{1}{3 4}, x = \frac{1}{2 3 4} - \frac{3}{2 3 4} i, x = \frac{1}{2 3 4} + \frac{3}{2 3 4} i, x = \frac{1}{3 7}, x = - \frac{1}{2 3 7} + \frac{3}{2 3 7} i, x = - \frac{1}{2 3 7} - \frac{3}{2 3 7} i

x = - \frac{1}{3 4}, x = \frac{1}{2 3 4} - \frac{3}{2 3 4} i, x = \frac{1}{2 3 4} + \frac{3}{2 3 4} i, x = \frac{1}{3 7}, x = - \frac{1}{2 3 7} + \frac{3}{2 3 7} i, x = - \frac{1}{2 3 7} - \frac{3}{2 3 7} i

验证解

找到无定义的点（奇点）:

x = 0

将不在定义域的点与解相综合:

x = - \frac{1}{3 4}, x = \frac{1}{2 3 4} - \frac{3}{2 3 4} i, x = \frac{1}{2 3 4} + \frac{3}{2 3 4} i, x = \frac{1}{3 7}, x = - \frac{1}{2 3 7} + \frac{3}{2 3 7} i, x = - \frac{1}{2 3 7} - \frac{3}{2 3 7} i

作图

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