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受欢迎的代数 >

x^2(x^2-16)-49(x^2-16)=0

解答

x^{2} (x^{2} - 16) - 49 (x^{2} - 16) = 0

解答

x = 7, x = - 7, x = 4, x = - 4

求解步骤

x^{2} (x^{2} - 16) - 49 (x^{2} - 16) = 0

展开

x^{2} (x^{2} - 16) - 49 (x^{2} - 16) : x^{4} - 65 x^{2} + 784

x^{4} - 65 x^{2} + 784 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - 65 u + 784 = 0

解

u^{2} - 65 u + 784 = 0 : u = 49, u = 16

u = 49, u = 16

代回

u = x^{2}

，求解

x

解

x^{2} = 49 : x = 7, x = - 7

解

x^{2} = 16 : x = 4, x = - 4

解为

x = 7, x = - 7, x = 4, x = - 4

作图

流行的例子

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