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受欢迎的代数 >

solvefor x,F=2xy^2x+(y+2yx^2)y

解答

求解

x, F = 2 x y^{2} x + (y + 2 y x^{2}) y

解答

x = \frac{F - y ^{2}}{2 y}, x = - \frac{F - y ^{2}}{2 y}; y \neq = 0

求解步骤

F = 2 x y^{2} x + (y + 2 y x^{2}) y

展开

2 x y^{2} x + (y + 2 y x^{2}) y : 4 x^{2} y^{2} + y^{2}

F = 4 x^{2} y^{2} + y^{2}

交换两边

4 x^{2} y^{2} + y^{2} = F

将

F

para o lado esquerdo

4 x^{2} y^{2} + y^{2} - F = 0

改写成标准形式

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

4 y^{2} x^{2} + y^{2} - F = 0

使用求根公式求解

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot 4 y ^{2} ( y ^{2} - F )}{2 \cdot 4 y ^{2}}

化简

0^{2} - 4 \cdot 4 y^{2} (y^{2} - F) : 4 y - y^{2} + F

x_{1, 2} = \frac{- 0 \pm 4 y - y ^{2} + F}{2 \cdot 4 y ^{2}}; y \neq = 0

将解分隔开

x_{1} = \frac{- 0 + 4 y - y ^{2} + F}{2 \cdot 4 y ^{2}}, x_{2} = \frac{- 0 - 4 y - y ^{2} + F}{2 \cdot 4 y ^{2}}

x = \frac{- 0 + 4 y - y ^{2} + F}{2 \cdot 4 y ^{2}} : \frac{F - y ^{2}}{2 y}

x = \frac{- 0 - 4 y - y ^{2} + F}{2 \cdot 4 y ^{2}} : - \frac{F - y ^{2}}{2 y}

二次方程组的解是:

x = \frac{F - y ^{2}}{2 y}, x = - \frac{F - y ^{2}}{2 y}; y \neq = 0

作图

流行的例子

64 x^{2} = 121

- \frac{1}{4} x^{2} + 4 x = - 2

solvefor x,x^2+y^2+z^2=6x-4y-10z

so l v e f or x, x^{2} + y^{2} + z^{2} = 6 x - 4 y - 10 z

solvefor x,z^2=4+4(x^2+y^2)

so l v e f or x, z^{2} = 4 + 4 (x^{2} + y^{2})

2 (x - 1)^{2} - 36 = 0