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受欢迎的代数 >

x^4-4x^2-77=0

解答

x^{4} - 4 x^{2} - 77 = 0

解答

x = 11, x = - 11, x = 7 i, x = - 7 i

求解步骤

x^{4} - 4 x^{2} - 77 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - 4 u - 77 = 0

解

u^{2} - 4 u - 77 = 0 : u = 11, u = - 7

u = 11, u = - 7

代回

u = x^{2}

，求解

x

解

x^{2} = 11 : x = 11, x = - 11

解

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

解为

x = 11, x = - 11, x = 7 i, x = - 7 i

作图

流行的例子

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

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

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0=3x^3-3x^2-18x

0 = 3 x^{3} - 3 x^{2} - 18 x

x^{4} - 64 i = 0

0=9x^5+72x^2+4x^4+32x

0 = 9 x^{5} + 72 x^{2} + 4 x^{4} + 32 x