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受欢迎的代数 >

x^8=10^{24}

解答

x^{8} = 1 0^{24}

解答

x = 1000, x = - 1000, x = 1000 i, x = - 1000 i, x = 5002 + 5002 i, x = - 5002 - 5002 i, x = 5002 - 5002 i, x = - 5002 + 5002 i

求解步骤

x^{8} = 1 0^{24}

用

u = x^{2}

和

u^{4} = x^{8}

改写方程式

u^{4} = 1 0^{24}

解

u^{4} = 1 0^{24} : u = 1000000, u = - 1000000, u = - 1 0^{12}, u = - - 1 0^{12}

u = 1000000, u = - 1000000, u = - 1 0^{12}, u = - - 1 0^{12}

代回

u = x^{2}

，求解

x

解

x^{2} = 1000000 : x = 1000, x = - 1000

解

x^{2} = - 1000000 : x = 1000 i, x = - 1000 i

解

x^{2} = - 1 0^{12} : x = 5002 + 5002 i, x = - 5002 - 5002 i

解

x^{2} = - - 1 0^{12} : x = 5002 - 5002 i, x = - 5002 + 5002 i

解为

x = 1000, x = - 1000, x = 1000 i, x = - 1000 i, x = 5002 + 5002 i, x = - 5002 - 5002 i, x = 5002 - 5002 i, x = - 5002 + 5002 i

作图

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