i(x)=-(x^2)/4+3450x

解答

i (x) = - \frac{x ^{2}}{4} + 3450 x

x = 0, x = 13800 - 4 i

求解步骤

i (x) = - \frac{x ^{2}}{4} + 3450 x

替代

x = a + bi

i (a + bi) = - \frac{( a + bi ) ^{2}}{4} + 3450 (a + bi)

在两边乘以

4

i (a + bi) \cdot 4 = - \frac{( a + bi ) ^{2}}{4} \cdot 4 + 3450 (a + bi) \cdot 4

乘开

- 4 b + 4 ia = (- a^{2} + b^{2} + 13800 a) + i (13800 b - 2 ab)

复数仅在实部和虚部均相等时才相等改写为方程组:

[- 4 b = - a^{2} + b^{2} + 13800 a 4 a = 13800 b - 2 ab]

[- 4 b = - a^{2} + b^{2} + 13800 a 4 a = 13800 b - 2 ab] : (a = 0, a = 13800, b = 0 b = - 4)

x = a + bi

代回

x = 0, x = 13800 - 4 i

(x - i) (x + i) = 0

x + y \cdot i = i

\frac{x}{1 + i} + \frac{y}{1 - 2 i} = 1

2 x + y + (x - y) i = 7 + 8 i

x^{2} - 5 i x + 6 = 0