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受欢迎的代数 >

1+2+3+n= 1/2 n(n+1)

解答

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

解答

n = 4, n = - 3

求解步骤

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

在两边乘以

2

2 + 4 + 6 + 2 n = n (n + 1)

2 n + 12 = n (n + 1)

展开

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

2 n + 12 = n^{2} + n

交换两边

n^{2} + n = 2 n + 12

将

12

para o lado esquerdo

n^{2} + n - 12 = 2 n

将

2 n

para o lado esquerdo

n^{2} - n - 12 = 0

使用求根公式求解

n_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot ( - 12 )}{2 \cdot 1}

(- 1)^{2} - 4 \cdot 1 \cdot (- 12) = 7

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

将解分隔开

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

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

n = \frac{- ( - 1 ) - 7}{2 \cdot 1} : - 3

二次方程组的解是:

n = 4, n = - 3

作图

流行的例子

15^2=20^2+x^2-2*20*x*0.75

1 5^{2} = 2 0^{2} + x^{2} - 2 \cdot 20 \cdot x \cdot 0.75

2 u^{2} + u - 1 = 0

s^{2} + 12 s + 400 = 0

x^{2} + 37 x = 0

-0.5a^2+243a-3280.5=0

- 0.5 a^{2} + 243 a - 3280.5 = 0