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受欢迎的代数 >

3x^2+3y^2=7,x^3+y^3=3

解答

3 x^{2} + 3 y^{2} = 7, x^{3} + y^{3} = 3

解答

x = \frac{7 + 33}{6}, x = \frac{6 - 1}{6}, x = \frac{6 + 1}{6}, x = - \frac{7 - 33}{6}, y = - \frac{33 - 3}{6} y = \frac{6 + 6}{6} y = \frac{- 6 + 6}{6} y = \frac{33 + 3}{6}

求解步骤

[3 x^{2} + 3 y^{2} = 7 x^{3} + y^{3} = 3]

对于

3 x^{2} + 3 y^{2} = 7

将

x

移到一边:

x = \frac{7 - 3 y ^{2}}{3}, x = - \frac{7 - 3 y ^{2}}{3}

将解

x = \frac{7 - 3 y ^{2}}{3}, x = - \frac{7 - 3 y ^{2}}{3}

代入

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

对于

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

，用

\frac{7 - 3 y ^{2}}{3}

替代

x : y = - \frac{33 - 3}{6}, y = \frac{6 + 6}{6}, y = \frac{- 6 + 6}{6}

对于

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

，用

- \frac{7 - 3 y ^{2}}{3}

替代

x : y = \frac{33 + 3}{6}

将解

y = - \frac{33 - 3}{6}, y = \frac{6 + 6}{6}, y = \frac{- 6 + 6}{6}, y = \frac{33 + 3}{6}

代入

3 x^{2} + 3 y^{2} = 7

对于

3 x^{2} + 3 y^{2} = 7

，用

- \frac{33 - 3}{6}

替代

y : x = \frac{7 + 33}{6}, x = - \frac{7 + 33}{6}

对于

3 x^{2} + 3 y^{2} = 7

，用

\frac{6 + 6}{6}

替代

y : x = \frac{6 - 1}{6}, x = - \frac{6 - 1}{6}

对于

3 x^{2} + 3 y^{2} = 7

，用

\frac{- 6 + 6}{6}

替代

y : x = \frac{6 + 1}{6}, x = - \frac{6 + 1}{6}

对于

3 x^{2} + 3 y^{2} = 7

，用

\frac{33 + 3}{6}

替代

y : x = \frac{7 - 33}{6}, x = - \frac{7 - 33}{6}

将解代入原方程进行验证

因而，

3 x^{2} + 3 y^{2} = 7, x^{3} + y^{3} = 3

最后的解是

x = \frac{7 + 33}{6}, x = \frac{6 - 1}{6}, x = \frac{6 + 1}{6}, x = - \frac{7 - 33}{6}, y = - \frac{33 - 3}{6} y = \frac{6 + 6}{6} y = \frac{- 6 + 6}{6} y = \frac{33 + 3}{6}

作图

流行的例子

x^2+3x+2=0,y^2+7y+12=0

x^{2} + 3 x + 2 = 0, y^{2} + 7 y + 12 = 0

4 x = 8, x - y = 6

8x+y=13,8x+y=13

8 x + y = 13, 8 x + y = 13

2x-y=-5,2x-y=-3

2 x - y = - 5, 2 x - y = - 3

x-y+z=2,x+3y+z=0

x - y + z = 2, x + 3 y + z = 0