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受欢迎的代数 >

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

解答

求解

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

解答

y = 1 + (x^{2} + 2) (x + 2), y = 1 - (x^{2} + 2) (x + 2)

求解步骤

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

将

3

para o lado esquerdo

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

将

2 x

para o lado esquerdo

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

将

2 x^{2}

para o lado esquerdo

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

将

x^{3}

para o lado esquerdo

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

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

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

二次方程组的解是:

y = 1 + (x^{2} + 2) (x + 2), y = 1 - (x^{2} + 2) (x + 2)

作图

流行的例子

-(2x)/((x^2+1)^2)<0

- \frac{2 x}{( x ^{2} + 1 ) ^{2}} < 0

x^{2} - 8 x - 8 = 0

因式分解 m^2+m

f a c t or m^{2} + m

化简 (-4x^2y^3)^4

s im pl i f y (- 4 x^{2} y^{3})^{4}

w^{2} - 7 = 0