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受欢迎的代数 >

-4n(n-2)=6(n+3)-11n^2

解答

- 4 n (n - 2) = 6 (n + 3) - 11 n^{2}

解答

n = - \frac{1 + 127}{7}, n = \frac{127 - 1}{7}

+1

十进制

n = - 1.75277 \dots, n = 1.46706 \dots

求解步骤

- 4 n (n - 2) = 6 (n + 3) - 11 n^{2}

展开

- 4 n (n - 2) : - 4 n^{2} + 8 n

展开

6 (n + 3) - 11 n^{2} : 6 n + 18 - 11 n^{2}

- 4 n^{2} + 8 n = 6 n + 18 - 11 n^{2}

交换两边

6 n + 18 - 11 n^{2} = - 4 n^{2} + 8 n

将

8 n

para o lado esquerdo

- 11 n^{2} - 2 n + 18 = - 4 n^{2}

将

4 n^{2}

para o lado esquerdo

- 7 n^{2} - 2 n + 18 = 0

使用求根公式求解

n_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 ( - 7 ) \cdot 18}{2 ( - 7 )}

(- 2)^{2} - 4 (- 7) \cdot 18 = 2127

n_{1, 2} = \frac{- ( - 2 ) \pm 2 127}{2 ( - 7 )}

将解分隔开

n_{1} = \frac{- ( - 2 ) + 2 127}{2 ( - 7 )}, n_{2} = \frac{- ( - 2 ) - 2 127}{2 ( - 7 )}

n = \frac{- ( - 2 ) + 2 127}{2 ( - 7 )} : - \frac{1 + 127}{7}

n = \frac{- ( - 2 ) - 2 127}{2 ( - 7 )} : \frac{127 - 1}{7}

二次方程组的解是:

n = - \frac{1 + 127}{7}, n = \frac{127 - 1}{7}

作图

流行的例子

2 (x + 2)^{2} = 72

- x^{2} + 7 x - 8 = 0

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

x^{2} - 3 = x - 2

n^{2} - 12 n - 107 = - 8