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受欢迎的代数 >

(x^2-1)(x^2-11)(x^2-21)(x^2-31)=-4224

解答

(x^{2} - 1) (x^{2} - 11) (x^{2} - 21) (x^{2} - 31) = - 4224

解答

x = 3, x = - 3, x = 23, x = - 23, x = 16 + 201, x = - 16 + 201, x = 16 - 201, x = - 16 - 201

+1

十进制

x = 3, x = - 3, x = 4.79583 \dots, x = - 4.79583 \dots, x = 5.49340 \dots, x = - 5.49340 \dots, x = 1.35001 \dots, x = - 1.35001 \dots

求解步骤

(x^{2} - 1) (x^{2} - 11) (x^{2} - 21) (x^{2} - 31) = - 4224

展开

(x^{2} - 1) (x^{2} - 11) (x^{2} - 21) (x^{2} - 31) : x^{8} - 64 x^{6} + 1286 x^{4} - 8384 x^{2} + 7161

x^{8} - 64 x^{6} + 1286 x^{4} - 8384 x^{2} + 7161 = - 4224

将

4224

para o lado esquerdo

x^{8} - 64 x^{6} + 1286 x^{4} - 8384 x^{2} + 11385 = 0

用

u = x^{2}, u^{2} = x^{4}, u^{3} = x^{6}

和

u^{4} = x^{8}

改写方程式

u^{4} - 64 u^{3} + 1286 u^{2} - 8384 u + 11385 = 0

解

u^{4} - 64 u^{3} + 1286 u^{2} - 8384 u + 11385 = 0 : u = 9, u = 23, u = 16 + 201, u = 16 - 201

u = 9, u = 23, u = 16 + 201, u = 16 - 201

代回

u = x^{2}

，求解

x

解

x^{2} = 9 : x = 3, x = - 3

解

x^{2} = 23 : x = 23, x = - 23

解

x^{2} = 16 + 201 : x = 16 + 201, x = - 16 + 201

解

x^{2} = 16 - 201 : x = 16 - 201, x = - 16 - 201

解为

x = 3, x = - 3, x = 23, x = - 23, x = 16 + 201, x = - 16 + 201, x = 16 - 201, x = - 16 - 201

作图

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