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受欢迎的代数 >

16x^4+25=41x^2

解答

16 x^{4} + 25 = 41 x^{2}

解答

x = \frac{5}{4}, x = - \frac{5}{4}, x = 1, x = - 1

+1

十进制

x = 1.25, x = - 1.25, x = 1, x = - 1

求解步骤

16 x^{4} + 25 = 41 x^{2}

将

41 x^{2}

para o lado esquerdo

16 x^{4} + 25 - 41 x^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

16 x^{4} - 41 x^{2} + 25 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

16 u^{2} - 41 u + 25 = 0

解

16 u^{2} - 41 u + 25 = 0 : u = \frac{25}{16}, u = 1

u = \frac{25}{16}, u = 1

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{25}{16} : x = \frac{5}{4}, x = - \frac{5}{4}

解

x^{2} = 1 : x = 1, x = - 1

解为

x = \frac{5}{4}, x = - \frac{5}{4}, x = 1, x = - 1

作图

流行的例子

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s^{4} + 5 s^{3} + 8 s^{2} + 3.93 s - 14 = 0

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3 = 0.03 t^{3} + 0.05 t^{2}

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2418 = 2330 \cdot (1 + r)^{15}

8m^3+32m^2-360m=0

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