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受欢迎的代数 >

1800-1505x^2+118x^4=0

解答

1800 - 1505 x^{2} + 118 x^{4} = 0

解答

x = \frac{1505 + 5 56617}{2 59}, x = - \frac{1505 + 5 56617}{2 59}, x = \frac{1505 - 5 56617}{2 59}, x = - \frac{1505 - 5 56617}{2 59}

+1

十进制

x = 3.37909 \dots, x = - 3.37909 \dots, x = 1.15583 \dots, x = - 1.15583 \dots

求解步骤

1800 - 1505 x^{2} + 118 x^{4} = 0

改写成标准形式

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

118 x^{4} - 1505 x^{2} + 1800 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

118 u^{2} - 1505 u + 1800 = 0

解

118 u^{2} - 1505 u + 1800 = 0 : u = \frac{1505 + 5 56617}{236}, u = \frac{1505 - 5 56617}{236}

u = \frac{1505 + 5 56617}{236}, u = \frac{1505 - 5 56617}{236}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{1505 + 5 56617}{236} : x = \frac{1505 + 5 56617}{2 59}, x = - \frac{1505 + 5 56617}{2 59}

解

x^{2} = \frac{1505 - 5 56617}{236} : x = \frac{1505 - 5 56617}{2 59}, x = - \frac{1505 - 5 56617}{2 59}

解为

x = \frac{1505 + 5 56617}{2 59}, x = - \frac{1505 + 5 56617}{2 59}, x = \frac{1505 - 5 56617}{2 59}, x = - \frac{1505 - 5 56617}{2 59}

作图

流行的例子

(x^{2} - 7) (x - 1) = 0

(x - 1)^{5} = - 32

x^{3} + 3 x - 10 = 0

9 t - t^{3} = 0

0=x^3-3x^2-16x+48

0 = x^{3} - 3 x^{2} - 16 x + 48