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人気のある代数 >

solvefor y,3x^2-2x+a-y^2+5xy+2=0

解

解く

y, 3 x^{2} - 2 x + a - y^{2} + 5 x y + 2 = 0

解

y = - \frac{- 5 x + 37 x ^{2} - 8 x + 4 a + 8}{2}, y = - \frac{- 5 x - 37 x ^{2} - 8 x + 4 a + 8}{2}

解答ステップ

3 x^{2} - 2 x + a - y^{2} + 5 x y + 2 = 0

標準的な形式で書く

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

- y^{2} + 5 x y + 3 x^{2} - 2 x + a + 2 = 0

解くとthe二次式

y_{1, 2} = \frac{- 5 x \pm ( 5 x ) ^{2} - 4 ( - 1 ) ( 3 x ^{2} - 2 x + a + 2 )}{2 ( - 1 )}

簡素化

(5 x)^{2} - 4 (- 1) (3 x^{2} - 2 x + a + 2) : 37 x^{2} - 8 x + 4 a + 8

y_{1, 2} = \frac{- 5 x \pm 37 x ^{2} - 8 x + 4 a + 8}{2 ( - 1 )}

解を分離する

y_{1} = \frac{- 5 x + 37 x ^{2} - 8 x + 4 a + 8}{2 ( - 1 )}, y_{2} = \frac{- 5 x - 37 x ^{2} - 8 x + 4 a + 8}{2 ( - 1 )}

y = \frac{- 5 x + 37 x ^{2} - 8 x + 4 a + 8}{2 ( - 1 )} : - \frac{- 5 x + 37 x ^{2} - 8 x + 4 a + 8}{2}

y = \frac{- 5 x - 37 x ^{2} - 8 x + 4 a + 8}{2 ( - 1 )} : - \frac{- 5 x - 37 x ^{2} - 8 x + 4 a + 8}{2}

二次equationの解:

y = - \frac{- 5 x + 37 x ^{2} - 8 x + 4 a + 8}{2}, y = - \frac{- 5 x - 37 x ^{2} - 8 x + 4 a + 8}{2}

グラフ

人気の例

3 x^{2} - 2 x = 6

y^{2} + 5 y - 6 = 0

1/2 (x+4)^2-3=29

\frac{1}{2} (x + 4)^{2} - 3 = 29

x^{2} - 12 x - 12 = - 39

solvefor x,x^2-2x-1=0

so l v e f or x, x^{2} - 2 x - 1 = 0