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受欢迎的代数 >

(x^2-6)^2=-3x^2+18

解答

(x^{2} - 6)^{2} = - 3 x^{2} + 18

解答

x = 6, x = - 6, x = 3, x = - 3

+1

十进制

x = 2.44948 \dots, x = - 2.44948 \dots, x = 1.73205 \dots, x = - 1.73205 \dots

求解步骤

(x^{2} - 6)^{2} = - 3 x^{2} + 18

展开

(x^{2} - 6)^{2} : x^{4} - 12 x^{2} + 36

x^{4} - 12 x^{2} + 36 = - 3 x^{2} + 18

将

18

para o lado esquerdo

x^{4} - 12 x^{2} + 18 = - 3 x^{2}

将

3 x^{2}

para o lado esquerdo

x^{4} - 9 x^{2} + 18 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - 9 u + 18 = 0

解

u^{2} - 9 u + 18 = 0 : u = 6, u = 3

u = 6, u = 3

代回

u = x^{2}

，求解

x

解

x^{2} = 6 : x = 6, x = - 6

解

x^{2} = 3 : x = 3, x = - 3

解为

x = 6, x = - 6, x = 3, x = - 3

作图

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