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受欢迎的代数 >

solvefor y,4x^2+5xy+y^2+3x-2y-7=0

解答

求解

y, 4 x^{2} + 5 x y + y^{2} + 3 x - 2 y - 7 = 0

解答

y = \frac{- 5 x + 2 + 9 x ^{2} - 32 x + 32}{2}, y = \frac{- 5 x + 2 - 9 x ^{2} - 32 x + 32}{2}

求解步骤

4 x^{2} + 5 x y + y^{2} + 3 x - 2 y - 7 = 0

改写成标准形式

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

y^{2} + (5 x - 2) y + 4 x^{2} + 3 x - 7 = 0

使用求根公式求解

y_{1, 2} = \frac{- ( 5 x - 2 ) \pm ( 5 x - 2 ) ^{2} - 4 \cdot 1 \cdot ( 4 x ^{2} + 3 x - 7 )}{2 \cdot 1}

化简

(5 x - 2)^{2} - 4 \cdot 1 \cdot (4 x^{2} + 3 x - 7) : 9 x^{2} - 32 x + 32

y_{1, 2} = \frac{- ( 5 x - 2 ) \pm 9 x ^{2} - 32 x + 32}{2 \cdot 1}

将解分隔开

y_{1} = \frac{- ( 5 x - 2 ) + 9 x ^{2} - 32 x + 32}{2 \cdot 1}, y_{2} = \frac{- ( 5 x - 2 ) - 9 x ^{2} - 32 x + 32}{2 \cdot 1}

y = \frac{- ( 5 x - 2 ) + 9 x ^{2} - 32 x + 32}{2 \cdot 1} : \frac{- 5 x + 2 + 9 x ^{2} - 32 x + 32}{2}

y = \frac{- ( 5 x - 2 ) - 9 x ^{2} - 32 x + 32}{2 \cdot 1} : \frac{- 5 x + 2 - 9 x ^{2} - 32 x + 32}{2}

二次方程组的解是:

y = \frac{- 5 x + 2 + 9 x ^{2} - 32 x + 32}{2}, y = \frac{- 5 x + 2 - 9 x ^{2} - 32 x + 32}{2}

作图

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