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受欢迎的代数 >

-1/4 x^2-4/3 x+7=0

解答

- \frac{1}{4} x^{2} - \frac{4}{3} x + 7 = 0

解答

x = - \frac{2 ( 4 + 79 )}{3}, x = \frac{2 ( 79 - 4 )}{3}

+1

十进制

x = - 8.59212 \dots, x = 3.25879 \dots

求解步骤

- \frac{1}{4} x^{2} - \frac{4}{3} x + 7 = 0

找到

4, 3

的最小公倍数:

12

乘以最小公倍数=

12

- \frac{1}{4} x^{2} \cdot 12 - \frac{4}{3} x \cdot 12 + 7 \cdot 12 = 0 \cdot 12

化简

- 3 x^{2} - 16 x + 84 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 ( - 3 ) \cdot 84}{2 ( - 3 )}

(- 16)^{2} - 4 (- 3) \cdot 84 = 479

x_{1, 2} = \frac{- ( - 16 ) \pm 4 79}{2 ( - 3 )}

将解分隔开

x_{1} = \frac{- ( - 16 ) + 4 79}{2 ( - 3 )}, x_{2} = \frac{- ( - 16 ) - 4 79}{2 ( - 3 )}

x = \frac{- ( - 16 ) + 4 79}{2 ( - 3 )} : - \frac{2 ( 4 + 79 )}{3}

x = \frac{- ( - 16 ) - 4 79}{2 ( - 3 )} : \frac{2 ( 79 - 4 )}{3}

二次方程组的解是:

x = - \frac{2 ( 4 + 79 )}{3}, x = \frac{2 ( 79 - 4 )}{3}

作图

流行的例子

(2k+2)x^2+(4-4k)x+k-2=0

(2 k + 2) x^{2} + (4 - 4 k) x + k - 2 = 0

2 d^{2} - 8 d + 19 = 6 d

12 x^{2} + 12 x - 6 = 0

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

x^{2} - 5 x + 9 = 3