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受欢迎的代数 >

solvefor x,x^2-2xy+3y^2=4

解答

求解

x, x^{2} - 2 x y + 3 y^{2} = 4

解答

x = \frac{2 y + - 8 y ^{2} + 16}{2}, x = \frac{2 y - - 8 y ^{2} + 16}{2}

求解步骤

x^{2} - 2 x y + 3 y^{2} = 4

将

4

para o lado esquerdo

x^{2} - 2 x y + 3 y^{2} - 4 = 0

改写成标准形式

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

x^{2} - 2 y x + 3 y^{2} - 4 = 0

使用求根公式求解

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

化简

(- 2 y)^{2} - 4 \cdot 1 \cdot (3 y^{2} - 4) : - 8 y^{2} + 16

x_{1, 2} = \frac{- ( - 2 y ) \pm - 8 y ^{2} + 16}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( - 2 y ) + - 8 y ^{2} + 16}{2 \cdot 1}, x_{2} = \frac{- ( - 2 y ) - - 8 y ^{2} + 16}{2 \cdot 1}

x = \frac{- ( - 2 y ) + - 8 y ^{2} + 16}{2 \cdot 1} : \frac{2 y + - 8 y ^{2} + 16}{2}

x = \frac{- ( - 2 y ) - - 8 y ^{2} + 16}{2 \cdot 1} : \frac{2 y - - 8 y ^{2} + 16}{2}

二次方程组的解是:

x = \frac{2 y + - 8 y ^{2} + 16}{2}, x = \frac{2 y - - 8 y ^{2} + 16}{2}

作图

流行的例子

y^{2} - 2 y = 15

completesquare x^2+4x-21=0

co m pl e t es q u a re x^{2} + 4 x - 21 = 0

0 = (x - 2) (x + 4)

solvefor x,x^2-10x+25=0

so l v e f or x, x^{2} - 10 x + 25 = 0

solvefor x,z=(12x-2x^2)+22y

so l v e f or x, z = (12 x - 2 x^{2}) + 22 y