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受欢迎的代数 >

64j^6-27j^9=0

解答

64 j^{6} - 27 j^{9} = 0

解答

j = 0, j = 3 \frac{64}{27}, j = 3 \frac{64}{27} \frac{- 1 + 3 i}{2}, j = 3 \frac{64}{27} \frac{- 1 - 3 i}{2}

求解步骤

64 j^{6} - 27 j^{9} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 27 j^{9} + 64 j^{6} = 0

用

u = j^{3}, u^{2} = j^{6}

和

u^{3} = j^{9}

改写方程式

- 27 u^{3} + 64 u^{2} = 0

解

- 27 u^{3} + 64 u^{2} = 0 : u = 0, u = \frac{64}{27}

u = 0, u = \frac{64}{27}

代回

u = j^{3}

，求解

j

解

j^{3} = 0 : j = 0

解

j^{3} = \frac{64}{27} : j = 3 \frac{64}{27}, j = 3 \frac{64}{27} \frac{- 1 + 3 i}{2}, j = 3 \frac{64}{27} \frac{- 1 - 3 i}{2}

解为

j = 0, j = 3 \frac{64}{27}, j = 3 \frac{64}{27} \frac{- 1 + 3 i}{2}, j = 3 \frac{64}{27} \frac{- 1 - 3 i}{2}

作图

流行的例子

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