solvefor y,six^2+8y=y^2

解答

求解

y, s i x^{2} + 8 y = y^{2}

无解

求解步骤

s i x^{2} + 8 y = y^{2}

替代

y = x + v i

s i x^{2} + 8 (x + v i) = (x + v i)^{2}

乘开

8 x + i (8 v + s x^{2}) = (x^{2} - v^{2}) + 2 i xv

复数仅在实部和虚部均相等时才相等改写为方程组:

[8 x = x^{2} - v^{2} 8 v + s x^{2} = 2 xv]

[8 x = x^{2} - v^{2} 8 v + s x^{2} = 2 xv] : 无解

y = x + v i

代回

无解

(x + y i)^{2} = 2 + 2 i 3

- 3 + y i = x + 6 i

40 - w^{2} - 2 w \cdot i = 0

x^{2} - x i - 1 = 0

\frac{2 x}{1 + x - y i} = 3 - 4 i