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受欢迎的代数 >

sqrt(3)y^2+0.685y-2.12=0

解答

3 y^{2} + 0.685 y - 2.12 = 0

解答

y = \frac{- 137 + 200 3 \frac{18769}{120000} + \frac{212}{25 3}}{400 3}, y = \frac{- 137 - 200 3 \frac{18769}{120000} + \frac{212}{25 3}}{400 3}

+1

十进制

y = 0.92612 \dots, y = - 1.32161 \dots

求解步骤

3 y^{2} + 0.685 y - 2.12 = 0

在两边乘以

1000

10003 y^{2} + 685 y - 2120 = 0

两边除以

10003

\frac{1000 3 y ^{2}}{1000 3} + \frac{685 y}{1000 3} - \frac{2120}{1000 3} = \frac{0}{1000 3}

改写成标准形式

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

y^{2} + \frac{137 y}{200 3} - \frac{53}{25 3} = 0

使用求根公式求解

y_{1, 2} = \frac{- \frac{137}{200 3} \pm ( \frac{137}{200 3} ) ^{2} - 4 \cdot 1 \cdot ( - \frac{53}{25 3} )}{2 \cdot 1}

(\frac{137}{200 3})^{2} - 4 \cdot 1 \cdot (- \frac{53}{25 3}) = \frac{18769}{120000} + \frac{212}{25 3}

y_{1, 2} = \frac{- \frac{137}{200 3} \pm \frac{18769}{120000} + \frac{212}{25 3}}{2 \cdot 1}

将解分隔开

y_{1} = \frac{- \frac{137}{200 3} + \frac{18769}{120000} + \frac{212}{25 3}}{2 \cdot 1}, y_{2} = \frac{- \frac{137}{200 3} - \frac{18769}{120000} + \frac{212}{25 3}}{2 \cdot 1}

y = \frac{- \frac{137}{200 3} + \frac{18769}{120000} + \frac{212}{25 3}}{2 \cdot 1} : \frac{- 137 + 200 3 \frac{18769}{120000} + \frac{212}{25 3}}{400 3}

y = \frac{- \frac{137}{200 3} - \frac{18769}{120000} + \frac{212}{25 3}}{2 \cdot 1} : \frac{- 137 - 200 3 \frac{18769}{120000} + \frac{212}{25 3}}{400 3}

二次方程组的解是:

y = \frac{- 137 + 200 3 \frac{18769}{120000} + \frac{212}{25 3}}{400 3}, y = \frac{- 137 - 200 3 \frac{18769}{120000} + \frac{212}{25 3}}{400 3}

作图

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