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受欢迎的代数 >

(y^2-1)^2+3(y^2-1)-18=0

解答

(y^{2} - 1)^{2} + 3 (y^{2} - 1) - 18 = 0

解答

y = 2, y = - 2, y = 5 i, y = - 5 i

求解步骤

(y^{2} - 1)^{2} + 3 (y^{2} - 1) - 18 = 0

展开

(y^{2} - 1)^{2} + 3 (y^{2} - 1) - 18 : y^{4} + y^{2} - 20

y^{4} + y^{2} - 20 = 0

用

u = y^{2}

和

u^{2} = y^{4}

改写方程式

u^{2} + u - 20 = 0

解

u^{2} + u - 20 = 0 : u = 4, u = - 5

u = 4, u = - 5

代回

u = y^{2}

，求解

y

解

y^{2} = 4 : y = 2, y = - 2

解

y^{2} = - 5 : y = 5 i, y = - 5 i

解为

y = 2, y = - 2, y = 5 i, y = - 5 i

作图

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