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人気のある代数 >

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

解

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

解

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}

解答ステップ

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

以下のために

x

を分離:

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

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

の解を以下に当てはめる:

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

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

では,

x

を

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

に置き換える:

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

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

では,

x

を

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

に置き換える:

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

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

の解を以下に当てはめる:

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

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

では,

y

を

- \frac{33 - 3}{6}

に置き換える:

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

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

では,

y

を

\frac{6 + 6}{6}

に置き換える:

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

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

では,

y

を

\frac{- 6 + 6}{6}

に置き換える:

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

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

では,

y

を

\frac{33 + 3}{6}

に置き換える:

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

元のequationに当てはめて解を検算する

ゆえに,

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

の最終的な解は

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}

グラフ

人気の例

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