2x^2+(8-2n)x+11=0

解答

2 x^{2} + (8 - 2 n) x + 11 = 0

x = \frac{- 4 + n + n ^{2} - 8 n - 6}{2}, x = \frac{- 4 + n - n ^{2} - 8 n - 6}{2}

求解步骤

2 x^{2} + (8 - 2 n) x + 11 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 8 - 2 n ) \pm ( 8 - 2 n ) ^{2} - 4 \cdot 2 \cdot 11}{2 \cdot 2}

化简

(8 - 2 n)^{2} - 4 \cdot 2 \cdot 11 : 2 n^{2} - 8 n - 6

x_{1, 2} = \frac{- ( 8 - 2 n ) \pm 2 n ^{2} - 8 n - 6}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( 8 - 2 n ) + 2 n ^{2} - 8 n - 6}{2 \cdot 2}, x_{2} = \frac{- ( 8 - 2 n ) - 2 n ^{2} - 8 n - 6}{2 \cdot 2}

x = \frac{- ( 8 - 2 n ) + 2 n ^{2} - 8 n - 6}{2 \cdot 2} : \frac{- 4 + n + n ^{2} - 8 n - 6}{2}

x = \frac{- ( 8 - 2 n ) - 2 n ^{2} - 8 n - 6}{2 \cdot 2} : \frac{- 4 + n - n ^{2} - 8 n - 6}{2}

二次方程组的解是:

x = \frac{- 4 + n + n ^{2} - 8 n - 6}{2}, x = \frac{- 4 + n - n ^{2} - 8 n - 6}{2}

16 x^{2} + 4 x = 0

5 x^{2} - 435 x + 5900 = 0

x^{2} + \frac{5000}{15000} x + \frac{3500}{15000} = 0

4 x^{2} - 12 x + 12 = 0

so l v e f or 0 = 2 x^{2} - 6 x + 2, x