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受欢迎的代数 >

solvefor y,x^2-xy+1/2 y^2=3

解答

求解

y, x^{2} - x y + \frac{1}{2} y^{2} = 3

解答

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

求解步骤

x^{2} - x y + \frac{1}{2} y^{2} = 3

在两边乘以

2

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

将

6

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

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

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

二次方程组的解是:

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

作图

流行的例子

(3 x - 6)^{2} = - 48

y^{2} + 9 y + 2 = 8 y + 58

solvefor x,3x^2-5x-1=0

so l v e f or x, 3 x^{2} - 5 x - 1 = 0

x^{2} - 16 x + 56 = 0

9 x^{2} + 14 x - 15 = 0