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受欢迎的代数 >

1+3+5+(2n+1)=n^2

解答

1 + 3 + 5 + (2 n + 1) = n^{2}

解答

n = 1 + 11, n = 1 - 11

+1

十进制

n = 4.31662 \dots, n = - 2.31662 \dots

求解步骤

1 + 3 + 5 + (2 n + 1) = n^{2}

整理后得

2 n + 10 = n^{2}

交换两边

n^{2} = 2 n + 10

将

10

para o lado esquerdo

n^{2} - 10 = 2 n

将

2 n

para o lado esquerdo

n^{2} - 10 - 2 n = 0

改写成标准形式

a x^{2} + b x + c = 0

n^{2} - 2 n - 10 = 0

使用求根公式求解

n_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 10 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 10) = 211

n_{1, 2} = \frac{- ( - 2 ) \pm 2 11}{2 \cdot 1}

将解分隔开

n_{1} = \frac{- ( - 2 ) + 2 11}{2 \cdot 1}, n_{2} = \frac{- ( - 2 ) - 2 11}{2 \cdot 1}

n = \frac{- ( - 2 ) + 2 11}{2 \cdot 1} : 1 + 11

n = \frac{- ( - 2 ) - 2 11}{2 \cdot 1} : 1 - 11

二次方程组的解是:

n = 1 + 11, n = 1 - 11

作图

流行的例子

solvefor x,x^2+2ax+a^2-n=0

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

x^{2} + 2 x + 65 = 0

x^{2} - 10 x = - 11

x^{2} - 10 x = - 13

x^{2} - 10 x = - 15