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受欢迎的代数 >

(72)4=n^8

解答

(72) 4 = n^{8}

解答

n = 2342, n = - 2342, n = 8 2^{5} 43 i, n = - 8 2^{5} 43 i, n = 4382 + 8243 i, n = - 4382 - 8243 i, n = 4382 - 8243 i, n = - 4382 + 4382 i

求解步骤

(72) \cdot 4 = n^{8}

交换两边

n^{8} = (72) \cdot 4

化简

(72) \cdot 4 : 288

用

u = n^{2}

和

u^{4} = n^{8}

改写方程式

u^{4} = 288

解

u^{4} = 288 : u = 2342, u = - 2342, u = 2342 i, u = - 2342 i

u = 2342, u = - 2342, u = 2342 i, u = - 2342 i

代回

u = n^{2}

，求解

n

解

n^{2} = 2342 : n = 2342, n = - 2342

解

n^{2} = - 2342 : n = 8 2^{5} 43 i, n = - 8 2^{5} 43 i

解

n^{2} = 2342 i : n = 4382 + 8243 i, n = - 4382 - 8243 i

解

n^{2} = - 2342 i : n = 4382 - 8243 i, n = - 4382 + 4382 i

解为

n = 2342, n = - 2342, n = 8 2^{5} 43 i, n = - 8 2^{5} 43 i, n = 4382 + 8243 i, n = - 4382 - 8243 i, n = 4382 - 8243 i, n = - 4382 + 4382 i

作图

流行的例子

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