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受欢迎的代数 >

1+4+7+(3n-2)= n/2 (3n-1)

解答

1 + 4 + 7 + (3 n - 2) = \frac{n}{2} (3 n - 1)

解答

n = 4, n = - \frac{5}{3}

+1

十进制

n = 4, n = - 1.66666 \dots

求解步骤

1 + 4 + 7 + (3 n - 2) = \frac{n}{2} (3 n - 1)

在两边乘以

2

2 + 8 + 14 + 2 (3 n - 2) = n (3 n - 1)

展开

2 + 8 + 14 + 2 (3 n - 2) : 6 n + 20

展开

n (3 n - 1) : 3 n^{2} - n

6 n + 20 = 3 n^{2} - n

交换两边

3 n^{2} - n = 6 n + 20

将

20

para o lado esquerdo

3 n^{2} - n - 20 = 6 n

将

6 n

para o lado esquerdo

3 n^{2} - 7 n - 20 = 0

使用求根公式求解

n_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 3 ( - 20 )}{2 \cdot 3}

(- 7)^{2} - 4 \cdot 3 (- 20) = 17

n_{1, 2} = \frac{- ( - 7 ) \pm 17}{2 \cdot 3}

将解分隔开

n_{1} = \frac{- ( - 7 ) + 17}{2 \cdot 3}, n_{2} = \frac{- ( - 7 ) - 17}{2 \cdot 3}

n = \frac{- ( - 7 ) + 17}{2 \cdot 3} : 4

n = \frac{- ( - 7 ) - 17}{2 \cdot 3} : - \frac{5}{3}

二次方程组的解是:

n = 4, n = - \frac{5}{3}

作图

流行的例子

- 3 x^{2} + 6 x = 4

7 n^{2} - 19 = 5 n

(x + 7) (x + 5) = 3

因式分解 6x^2-7x-3=0

f a c t or 6 x^{2} - 7 x - 3 = 0

x (x - 6) = - 3