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受欢迎的代数 >

2nx^2=x+1/n

解答

2 n x^{2} = x + \frac{1}{n}

解答

x = \frac{1}{n}, x = - \frac{1}{2 n}; n \neq = 0

求解步骤

2 n x^{2} = x + \frac{1}{n}

在两边乘以

n

2 n^{2} x^{2} = n x + 1; n \neq = 0

将

1

para o lado esquerdo

2 n^{2} x^{2} - 1 = n x; n \neq = 0

将

n x

para o lado esquerdo

2 n^{2} x^{2} - 1 - n x = 0; n \neq = 0

改写成标准形式

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

2 n^{2} x^{2} - n x - 1 = 0; n \neq = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - n ) \pm ( - n ) ^{2} - 4 \cdot 2 n ^{2} ( - 1 )}{2 \cdot 2 n ^{2}}

化简

(- n)^{2} - 4 \cdot 2 n^{2} (- 1) : 3 n

x_{1, 2} = \frac{- ( - n ) \pm 3 n}{2 \cdot 2 n ^{2}}; n \neq = 0

将解分隔开

x_{1} = \frac{- ( - n ) + 3 n}{2 \cdot 2 n ^{2}}, x_{2} = \frac{- ( - n ) - 3 n}{2 \cdot 2 n ^{2}}

x = \frac{- ( - n ) + 3 n}{2 \cdot 2 n ^{2}} : \frac{1}{n}

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

二次方程组的解是:

x = \frac{1}{n}, x = - \frac{1}{2 n}; n \neq = 0

作图

流行的例子

- x^{2} - 5 x - 4 = 0

因式分解 x^2+8x+12=0

f a c t or x^{2} + 8 x + 12 = 0

4 (x + 1)^{2} = 36

x^{2} + 4 = 10

x^{2} + 4 = 12