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受欢迎的代数 >

1003x^2+(1003+2sqrt(1001))x+199=0

解答

1003 x^{2} + (1003 + 21001) x + 199 = 0

解答

x = \frac{- 1003 - 2 1001 + 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}, x = \frac{- 1003 - 2 1001 - 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

+1

十进制

x = - 0.24148 \dots, x = - 0.82160 \dots

求解步骤

1003 x^{2} + (1003 + 21001) x + 199 = 0

两边除以

1003

\frac{1003 x ^{2}}{1003} + \frac{( 1003 + 2 1001 ) x}{1003} + \frac{199}{1003} = \frac{0}{1003}

改写成标准形式

a x^{2} + b x + c = 0

x^{2} + (1 + \frac{2 1001}{1003}) x + \frac{199}{1003} = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 1 + \frac{2 1001}{1003} ) \pm ( 1 + \frac{2 1001}{1003} ) ^{2} - 4 \cdot 1 \cdot \frac{199}{1003}}{2 \cdot 1}

(1 + \frac{2 1001}{1003})^{2} - 4 \cdot 1 \cdot \frac{199}{1003} = \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}

x_{1, 2} = \frac{- ( 1 + \frac{2 1001}{1003} ) \pm \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( 1 + \frac{2 1001}{1003} ) + \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1}, x_{2} = \frac{- ( 1 + \frac{2 1001}{1003} ) - \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1}

x = \frac{- ( 1 + \frac{2 1001}{1003} ) + \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1} : \frac{- 1003 - 2 1001 + 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

x = \frac{- ( 1 + \frac{2 1001}{1003} ) - \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1} : \frac{- 1003 - 2 1001 - 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

二次方程组的解是:

x = \frac{- 1003 - 2 1001 + 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}, x = \frac{- 1003 - 2 1001 - 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

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