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人気のある代数 >

solvefor y,x^3-3x^2y+y^2=1

解

解く

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

解

y = \frac{3 x ^{2} + 9 x ^{4} - 4 ( x ^{3} - 1 )}{2}, y = \frac{3 x ^{2} - 9 x ^{4} - 4 ( x ^{3} - 1 )}{2}

解答ステップ

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

1

を左側に移動します

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

標準的な形式で書く

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

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

解くとthe二次式

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

簡素化

(- 3 x^{2})^{2} - 4 \cdot 1 \cdot (x^{3} - 1) : 9 x^{4} - 4 (x^{3} - 1)

y_{1, 2} = \frac{- ( - 3 x ^{2} ) \pm 9 x ^{4} - 4 ( x ^{3} - 1 )}{2 \cdot 1}

解を分離する

y_{1} = \frac{- ( - 3 x ^{2} ) + 9 x ^{4} - 4 ( x ^{3} - 1 )}{2 \cdot 1}, y_{2} = \frac{- ( - 3 x ^{2} ) - 9 x ^{4} - 4 ( x ^{3} - 1 )}{2 \cdot 1}

y = \frac{- ( - 3 x ^{2} ) + 9 x ^{4} - 4 ( x ^{3} - 1 )}{2 \cdot 1} : \frac{3 x ^{2} + 9 x ^{4} - 4 ( x ^{3} - 1 )}{2}

y = \frac{- ( - 3 x ^{2} ) - 9 x ^{4} - 4 ( x ^{3} - 1 )}{2 \cdot 1} : \frac{3 x ^{2} - 9 x ^{4} - 4 ( x ^{3} - 1 )}{2}

二次equationの解:

y = \frac{3 x ^{2} + 9 x ^{4} - 4 ( x ^{3} - 1 )}{2}, y = \frac{3 x ^{2} - 9 x ^{4} - 4 ( x ^{3} - 1 )}{2}

グラフ

人気の例

(x-sqrt(5))^2=2sqrt(5)

(x - 5)^{2} = 25

(x + 1)^{2} = 75

solvefor y,x^2y^2=9

so l v e f or y, x^{2} y^{2} = 9

5 x^{2} - 291 x - 16 = 0

2 (x + 7)^{2} + 27 = 41