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受欢迎的代数 >

x^2-1=0,y^2+z=0,z^2+y=0

解答

x^{2} - 1 = 0, y^{2} + z = 0, z^{2} + y = 0

解答

x = 1, x = 1, x = 1, x = 1, y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i, z = 0 z = - 1 z = \frac{1}{2} + i \frac{3}{2} z = \frac{1}{2} - i \frac{3}{2}

求解步骤

x^{2} - 1 = 0 y^{2} + z = 0 z^{2} + y = 0

对于

y^{2} + z = 0

将

z

移到一边:

z = - y^{2}

将解

z = - y^{2}

代入

z^{2} + y = 0

对于

z^{2} + y = 0

，用

- y^{2}

替代

z : y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i

将解

y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i

代入

y^{2} + z = 0

对于

y^{2} + z = 0

，用

0

替代

y : z = 0

对于

y^{2} + z = 0

，用

- 1

替代

y : z = - 1

对于

y^{2} + z = 0

，用

\frac{1}{2} - \frac{3}{2} i

替代

y : z = \frac{1}{2} + i \frac{3}{2}

对于

y^{2} + z = 0

，用

\frac{1}{2} + \frac{3}{2} i

替代

y : z = \frac{1}{2} - i \frac{3}{2}

x^{2} - 1 = 0 : x = 1, x = - 1

将解代入原方程进行验证

因而，

x^{2} - 1 = 0, y^{2} + z = 0, z^{2} + y = 0

最后的解是

x = 1, x = 1, x = 1, x = 1, y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i, z = 0 z = - 1 z = \frac{1}{2} + i \frac{3}{2} z = \frac{1}{2} - i \frac{3}{2}

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(x + 3) (x - 2) = 4 (x - 2)

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