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受欢迎的代数 >

solvefor y,z=y^2+(x^3)/3+xy

解答

求解

y, z = y^{2} + \frac{x ^{3}}{3} + x y

解答

y = \frac{- 3 x + 9 x ^{2} - 12 ( x ^{3} - 3 z )}{6}, y = \frac{- 3 x - 9 x ^{2} - 12 ( x ^{3} - 3 z )}{6}

求解步骤

z = y^{2} + \frac{x ^{3}}{3} + x y

在两边乘以

3

3 z = 3 y^{2} + x^{3} + 3 y x

交换两边

3 y^{2} + x^{3} + 3 y x = 3 z

将

3 z

para o lado esquerdo

3 y^{2} + x^{3} + 3 y x - 3 z = 0

改写成标准形式

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

3 y^{2} + 3 x y + x^{3} - 3 z = 0

使用求根公式求解

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

化简

(3 x)^{2} - 4 \cdot 3 (x^{3} - 3 z) : 9 x^{2} - 12 (x^{3} - 3 z)

y_{1, 2} = \frac{- 3 x \pm 9 x ^{2} - 12 ( x ^{3} - 3 z )}{2 \cdot 3}

将解分隔开

y_{1} = \frac{- 3 x + 9 x ^{2} - 12 ( x ^{3} - 3 z )}{2 \cdot 3}, y_{2} = \frac{- 3 x - 9 x ^{2} - 12 ( x ^{3} - 3 z )}{2 \cdot 3}

y = \frac{- 3 x + 9 x ^{2} - 12 ( x ^{3} - 3 z )}{2 \cdot 3} : \frac{- 3 x + 9 x ^{2} - 12 ( x ^{3} - 3 z )}{6}

y = \frac{- 3 x - 9 x ^{2} - 12 ( x ^{3} - 3 z )}{2 \cdot 3} : \frac{- 3 x - 9 x ^{2} - 12 ( x ^{3} - 3 z )}{6}

二次方程组的解是:

y = \frac{- 3 x + 9 x ^{2} - 12 ( x ^{3} - 3 z )}{6}, y = \frac{- 3 x - 9 x ^{2} - 12 ( x ^{3} - 3 z )}{6}

作图

流行的例子

(20+2x)(10+2x)=200+64

(20 + 2 x) (10 + 2 x) = 200 + 64

11c^2+27c+14=2c^2

11 c^{2} + 27 c + 14 = 2 c^{2}

5 x^{2} + 10 x - 2 = 0

solvefor x,36x^2-36x+36y^2+24y+13=0

so l v e f or x, 36 x^{2} - 36 x + 36 y^{2} + 24 y + 13 = 0

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