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受欢迎的代数 >

x^2+((5-2x)/3)^2=2

解答

x^{2} + (\frac{5 - 2 x}{3})^{2} = 2

解答

x = 1, x = \frac{7}{13}

+1

十进制

x = 1, x = 0.53846 \dots

求解步骤

x^{2} + (\frac{5 - 2 x}{3})^{2} = 2

展开

x^{2} + (\frac{5 - 2 x}{3})^{2} : \frac{25}{9} - \frac{20 x}{9} + \frac{13 x ^{2}}{9}

\frac{25}{9} - \frac{20 x}{9} + \frac{13 x ^{2}}{9} = 2

将

2

para o lado esquerdo

\frac{25 - 20 x + 13 x ^{2}}{9} - 2 = 0

改写成标准形式

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

\frac{13 x ^{2}}{9} - \frac{20 x}{9} + \frac{25}{9} - 2 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - \frac{20}{9} ) \pm ( - \frac{20}{9} ) ^{2} - 4 \cdot \frac{13}{9} ( \frac{25}{9} - 2 )}{2 \cdot \frac{13}{9}}

(- \frac{20}{9})^{2} - 4 \cdot \frac{13}{9} (\frac{25}{9} - 2) = \frac{2}{3}

x_{1, 2} = \frac{- ( - \frac{20}{9} ) \pm \frac{2}{3}}{2 \cdot \frac{13}{9}}

将解分隔开

x_{1} = \frac{- ( - \frac{20}{9} ) + \frac{2}{3}}{2 \cdot \frac{13}{9}}, x_{2} = \frac{- ( - \frac{20}{9} ) - \frac{2}{3}}{2 \cdot \frac{13}{9}}

x = \frac{- ( - \frac{20}{9} ) + \frac{2}{3}}{2 \frac{13}{9}} : 1

x = \frac{- ( - \frac{20}{9} ) - \frac{2}{3}}{2 \frac{13}{9}} : \frac{7}{13}

二次方程组的解是:

x = 1, x = \frac{7}{13}

作图

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