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受欢迎的代数 >

solvefor y,b=(x^2-2xy-3)(-x*y)

解答

求解

y, b = (x^{2} - 2 x y - 3) (- x \cdot y)

解答

y = \frac{x ^{3} - 3 x + ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{4 x ^{2}}, y = \frac{x ^{3} - 3 x - ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{4 x ^{2}}; x \neq = 0

求解步骤

b = (x^{2} - 2 x y - 3) (- x y)

展开

(x^{2} - 2 x y - 3) (- x y) : - y x^{3} + 2 y^{2} x^{2} + 3 y x

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

交换两边

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

将

b

para o lado esquerdo

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

改写成标准形式

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

2 x^{2} y^{2} + (- x^{3} + 3 x) y - b = 0

使用求根公式求解

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

化简

(- x^{3} + 3 x)^{2} - 4 \cdot 2 x^{2} (- b) : (- x^{3} + 3 x)^{2} + 8 b x^{2}

y_{1, 2} = \frac{- ( - x ^{3} + 3 x ) \pm ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{2 \cdot 2 x ^{2}}; x \neq = 0

将解分隔开

y_{1} = \frac{- ( - x ^{3} + 3 x ) + ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{2 \cdot 2 x ^{2}}, y_{2} = \frac{- ( - x ^{3} + 3 x ) - ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{2 \cdot 2 x ^{2}}

y = \frac{- ( - x ^{3} + 3 x ) + ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{2 \cdot 2 x ^{2}} : \frac{x ^{3} - 3 x + ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{4 x ^{2}}

y = \frac{- ( - x ^{3} + 3 x ) - ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{2 \cdot 2 x ^{2}} : \frac{x ^{3} - 3 x - ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{4 x ^{2}}

二次方程组的解是:

y = \frac{x ^{3} - 3 x + ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{4 x ^{2}}, y = \frac{x ^{3} - 3 x - ( - x ^{3} + 3 x ) ^{2} + 8 b x ^{2}}{4 x ^{2}}; x \neq = 0

作图

流行的例子

140 = 110 (1 + r)^{2}

solvefor x,12x^2-26xy+12y^2=0

so l v e f or x, 12 x^{2} - 26 x y + 12 y^{2} = 0

solvefor y,y^2=x^2(1-x)

so l v e f or y, y^{2} = x^{2} (1 - x)

z^{1} + z^{2} - 2 = 0

(3)r=(x^2=9-3=5)

(3) r = (x^{2} = 9 - 3 = 5)