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受欢迎的代数 >

solvefor y,3x^2-6xy+y^2=2x-y

解答

求解

y, 3 x^{2} - 6 x y + y^{2} = 2 x - y

解答

y = \frac{6 x - 1 + 24 x ^{2} - 4 x + 1}{2}, y = \frac{6 x - 1 - 24 x ^{2} - 4 x + 1}{2}

求解步骤

3 x^{2} - 6 x y + y^{2} = 2 x - y

将

y

para o lado esquerdo

3 x^{2} - 6 x y + y^{2} + y = 2 x

将

2 x

para o lado esquerdo

3 x^{2} - 6 x y + y^{2} + y - 2 x = 0

改写成标准形式

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

y^{2} + (- 6 x + 1) y + 3 x^{2} - 2 x = 0

使用求根公式求解

y_{1, 2} = \frac{- ( - 6 x + 1 ) \pm ( - 6 x + 1 ) ^{2} - 4 \cdot 1 \cdot ( 3 x ^{2} - 2 x )}{2 \cdot 1}

化简

(- 6 x + 1)^{2} - 4 \cdot 1 \cdot (3 x^{2} - 2 x) : 24 x^{2} - 4 x + 1

y_{1, 2} = \frac{- ( - 6 x + 1 ) \pm 24 x ^{2} - 4 x + 1}{2 \cdot 1}

将解分隔开

y_{1} = \frac{- ( - 6 x + 1 ) + 24 x ^{2} - 4 x + 1}{2 \cdot 1}, y_{2} = \frac{- ( - 6 x + 1 ) - 24 x ^{2} - 4 x + 1}{2 \cdot 1}

y = \frac{- ( - 6 x + 1 ) + 24 x ^{2} - 4 x + 1}{2 \cdot 1} : \frac{6 x - 1 + 24 x ^{2} - 4 x + 1}{2}

y = \frac{- ( - 6 x + 1 ) - 24 x ^{2} - 4 x + 1}{2 \cdot 1} : \frac{6 x - 1 - 24 x ^{2} - 4 x + 1}{2}

二次方程组的解是:

y = \frac{6 x - 1 + 24 x ^{2} - 4 x + 1}{2}, y = \frac{6 x - 1 - 24 x ^{2} - 4 x + 1}{2}

作图

流行的例子

3 y^{2} - 24 y - 41 = 0

(\frac{x}{4})^{2} - 0.16 = 0

roo t s x^{2} - 2 x - 5

3x+2=-2x^2+3x+6

3 x + 2 = - 2 x^{2} + 3 x + 6

3m^2+15m+25.5=0

3 m^{2} + 15 m + 25.5 = 0