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受欢迎的代数 >

(n(n+1))/2 =100

解答

\frac{n ( n + 1 )}{2} = 100

解答

n = \frac{- 1 + 3 89}{2}, n = \frac{- 1 - 3 89}{2}

+1

十进制

n = 13.65097 \dots, n = - 14.65097 \dots

求解步骤

\frac{n ( n + 1 )}{2} = 100

在两边乘以

2

n (n + 1) = 200

展开

n (n + 1) : n^{2} + n

n^{2} + n = 200

将

200

para o lado esquerdo

n^{2} + n - 200 = 0

使用求根公式求解

n_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 200 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 200) = 389

n_{1, 2} = \frac{- 1 \pm 3 89}{2 \cdot 1}

将解分隔开

n_{1} = \frac{- 1 + 3 89}{2 \cdot 1}, n_{2} = \frac{- 1 - 3 89}{2 \cdot 1}

n = \frac{- 1 + 3 89}{2 \cdot 1} : \frac{- 1 + 3 89}{2}

n = \frac{- 1 - 3 89}{2 \cdot 1} : \frac{- 1 - 3 89}{2}

二次方程组的解是:

n = \frac{- 1 + 3 89}{2}, n = \frac{- 1 - 3 89}{2}

作图

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