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受欢迎的代数 >

根 4x^2+7mnx-15m^2n^2

解答

根

4 x^{2} + 7 mn x - 15 m^{2} n^{2}

解答

x = \frac{5 mn}{4}, x = - 3 mn

求解步骤

4 x^{2} + 7 mn x - 15 m^{2} n^{2}

根与 X 轴相交

(y = 0)

4 x^{2} + 7 mn x - 15 m^{2} n^{2} = 0

使用求根公式求解

x_{1, 2} = \frac{- 7 mn \pm ( 7 mn ) ^{2} - 4 \cdot 4 ( - 15 m ^{2} n ^{2} )}{2 \cdot 4}

化简

(7 mn)^{2} - 4 \cdot 4 (- 15 m^{2} n^{2}) : 17 mn

x_{1, 2} = \frac{- 7 mn \pm 17 mn}{2 \cdot 4}

将解分隔开

x_{1} = \frac{- 7 mn + 17 mn}{2 \cdot 4}, x_{2} = \frac{- 7 mn - 17 mn}{2 \cdot 4}

x = \frac{- 7 mn + 17 mn}{2 \cdot 4} : \frac{5 mn}{4}

x = \frac{- 7 mn - 17 mn}{2 \cdot 4} : - 3 mn

二次方程组的解是:

x = \frac{5 mn}{4}, x = - 3 mn

作图

流行的例子

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so l v e f or y, 6 x^{2} y - 9 x^{2} + 23 x y - 6 x + 21 y + 80 = 0

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