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受欢迎的代数 >

1/2 X-(X-2)/4 = 1/2 (X*(2X-1)/3)

解答

\frac{1}{2} X - \frac{X - 2}{4} = \frac{1}{2} (X \cdot \frac{2 X - 1}{3})

解答

X = 2, X = - \frac{3}{4}

+1

十进制

X = 2, X = - 0.75

求解步骤

\frac{1}{2} X - \frac{X - 2}{4} = \frac{1}{2} (X \frac{2 X - 1}{3})

找到

2, 4

的最小公倍数:

4

乘以最小公倍数=

4

\frac{1}{2} X \cdot 4 - \frac{X - 2}{4} \cdot 4 = \frac{1}{2} X \frac{2 X - 1}{3} \cdot 4

化简

2 X - (X - 2) = \frac{2 X ( 2 X - 1 )}{3}

展开

2 X - (X - 2) : X + 2

展开

\frac{2 X ( 2 X - 1 )}{3} : \frac{4 X ^{2}}{3} - \frac{2 X}{3}

X + 2 = \frac{4 X ^{2}}{3} - \frac{2 X}{3}

交换两边

\frac{4 X ^{2}}{3} - \frac{2 X}{3} = X + 2

将

2

para o lado esquerdo

\frac{4 X ^{2} - 2 X}{3} - 2 = X

将

X

para o lado esquerdo

\frac{4 X ^{2} - 5 X}{3} - 2 = 0

改写成标准形式

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

\frac{4 X ^{2}}{3} - \frac{5 X}{3} - 2 = 0

使用求根公式求解

X_{1, 2} = \frac{- ( - \frac{5}{3} ) \pm ( - \frac{5}{3} ) ^{2} - 4 \cdot \frac{4}{3} ( - 2 )}{2 \cdot \frac{4}{3}}

(- \frac{5}{3})^{2} - 4 \cdot \frac{4}{3} (- 2) = \frac{11}{3}

X_{1, 2} = \frac{- ( - \frac{5}{3} ) \pm \frac{11}{3}}{2 \cdot \frac{4}{3}}

将解分隔开

X_{1} = \frac{- ( - \frac{5}{3} ) + \frac{11}{3}}{2 \cdot \frac{4}{3}}, X_{2} = \frac{- ( - \frac{5}{3} ) - \frac{11}{3}}{2 \cdot \frac{4}{3}}

X = \frac{- ( - \frac{5}{3} ) + \frac{11}{3}}{2 \frac{4}{3}} : 2

X = \frac{- ( - \frac{5}{3} ) - \frac{11}{3}}{2 \frac{4}{3}} : - \frac{3}{4}

二次方程组的解是:

X = 2, X = - \frac{3}{4}

作图

流行的例子

x^{2} - \frac{5}{2} x = - \frac{3}{2}

4 (x + 1)^{2} = 100

4 p^{2} + 4 p + 1 = 0

x^{2} + 12 x + 28 = 0

x^2-(2+sqrt(2))x+2sqrt(2)=0

x^{2} - (2 + 2) x + 22 = 0