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受欢迎的代数 >

4x^2=4x+1

解答

4 x^{2} = 4 x + 1

解答

x = \frac{1 + 2}{2}, x = \frac{1 - 2}{2}

+1

十进制

x = 1.20710 \dots, x = - 0.20710 \dots

求解步骤

4 x^{2} = 4 x + 1

将

1

para o lado esquerdo

4 x^{2} - 1 = 4 x

将

4 x

para o lado esquerdo

4 x^{2} - 1 - 4 x = 0

改写成标准形式

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

4 x^{2} - 4 x - 1 = 0

使用求根公式求解

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

(- 4)^{2} - 4 \cdot 4 (- 1) = 42

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

将解分隔开

x_{1} = \frac{- ( - 4 ) + 4 2}{2 \cdot 4}, x_{2} = \frac{- ( - 4 ) - 4 2}{2 \cdot 4}

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

x = \frac{- ( - 4 ) - 4 2}{2 \cdot 4} : \frac{1 - 2}{2}

二次方程组的解是:

x = \frac{1 + 2}{2}, x = \frac{1 - 2}{2}

作图

流行的例子

5 x^{2} = - 45 x

0 = - 2 x^{2} + 3 x - 1

因式分解 3x^2=12-16x

f a c t or 3 x^{2} = 12 - 16 x

n^{2} - 10 n - 8 = 0

根 25x^2+50x+169=0

roo t s 25 x^{2} + 50 x + 169 = 0