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受欢迎的代数 >

(x^2-5)/(2x+i)=0

解答

\frac{x ^{2} - 5}{2 x + i} = 0

解答

x = 5, x = - 5

+1

十进制

x = 2.23606 \dots, x = - 2.23606 \dots

求解步骤

\frac{x ^{2} - 5}{2 x + i} = 0

替代

x = a + bi

\frac{( a + bi ) ^{2} - 5}{2 ( a + bi ) + i} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

(a + bi)^{2} - 5 = 0

展开

(a + bi)^{2} - 5 : (a^{2} - b^{2} - 5) + 2 iab

(a^{2} - b^{2} - 5) + 2 iab = 0

将

0

改写成标准复数形式:

0 + 0 i

(a^{2} - b^{2} - 5) + 2 iab = 0 + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[a^{2} - b^{2} - 5 = 0 2 ab = 0]

[a^{2} - b^{2} - 5 = 0 2 ab = 0] : (a = 5, a = - 5, b = 0 b = 0)

x = a + bi

代回

x = 5, x = - 5

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