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受欢迎的代数 >

solvefor y,(x^3)/3+(y^2)/2-3x+2y=-1/6

解答

求解

y, \frac{x ^{3}}{3} + \frac{y ^{2}}{2} - 3 x + 2 y = - \frac{1}{6}

解答

y = \frac{- 12 + - 24 x ^{3} + 216 x + 132}{6}, y = \frac{- 12 - - 24 x ^{3} + 216 x + 132}{6}

求解步骤

\frac{x ^{3}}{3} + \frac{y ^{2}}{2} - 3 x + 2 y = - \frac{1}{6}

找到

3, 2, 6

的最小公倍数:

6

乘以最小公倍数=

6

\frac{x ^{3}}{3} \cdot 6 + \frac{y ^{2}}{2} \cdot 6 - 3 x \cdot 6 + 2 y \cdot 6 = - \frac{1}{6} \cdot 6

化简

2 x^{3} + 3 y^{2} - 18 x + 12 y = - 1

将

1

para o lado esquerdo

2 x^{3} + 3 y^{2} - 18 x + 12 y + 1 = 0

改写成标准形式

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

3 y^{2} + 12 y + 2 x^{3} - 18 x + 1 = 0

使用求根公式求解

y_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 3 ( 2 x ^{3} - 18 x + 1 )}{2 \cdot 3}

化简

1 2^{2} - 4 \cdot 3 (2 x^{3} - 18 x + 1) : - 24 x^{3} + 216 x + 132

y_{1, 2} = \frac{- 12 \pm - 24 x ^{3} + 216 x + 132}{2 \cdot 3}

将解分隔开

y_{1} = \frac{- 12 + - 24 x ^{3} + 216 x + 132}{2 \cdot 3}, y_{2} = \frac{- 12 - - 24 x ^{3} + 216 x + 132}{2 \cdot 3}

y = \frac{- 12 + - 24 x ^{3} + 216 x + 132}{2 \cdot 3} : \frac{- 12 + - 24 x ^{3} + 216 x + 132}{6}

y = \frac{- 12 - - 24 x ^{3} + 216 x + 132}{2 \cdot 3} : \frac{- 12 - - 24 x ^{3} + 216 x + 132}{6}

二次方程组的解是:

y = \frac{- 12 + - 24 x ^{3} + 216 x + 132}{6}, y = \frac{- 12 - - 24 x ^{3} + 216 x + 132}{6}

作图

流行的例子

- 3 x^{2} - 6 x - 6 = 0

4 x^{2} - 8 x - 4 = 0

x^{2} + 4 x + 85 = 0

x^{2} - 6 x = - x^{2} + 6 x

c^{2} = 15