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受欢迎的代数 >

(2x-1)(3x-2)-5(x-2)(x+2)=2(x-3)^2-2

解答

(2 x - 1) (3 x - 2) - 5 (x - 2) (x + 2) = 2 (x - 3)^{2} - 2

解答

x = - 1, x = 6

求解步骤

(2 x - 1) (3 x - 2) - 5 (x - 2) (x + 2) = 2 (x - 3)^{2} - 2

展开

(2 x - 1) (3 x - 2) - 5 (x - 2) (x + 2) : x^{2} - 7 x + 22

展开

2 (x - 3)^{2} - 2 : 2 x^{2} - 12 x + 16

x^{2} - 7 x + 22 = 2 x^{2} - 12 x + 16

将

16

para o lado esquerdo

x^{2} - 7 x + 6 = 2 x^{2} - 12 x

将

12 x

para o lado esquerdo

x^{2} + 5 x + 6 = 2 x^{2}

将

2 x^{2}

para o lado esquerdo

- x^{2} + 5 x + 6 = 0

使用求根公式求解

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 ( - 1 ) \cdot 6}{2 ( - 1 )}

5^{2} - 4 (- 1) \cdot 6 = 7

x_{1, 2} = \frac{- 5 \pm 7}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- 5 + 7}{2 ( - 1 )}, x_{2} = \frac{- 5 - 7}{2 ( - 1 )}

x = \frac{- 5 + 7}{2 ( - 1 )} : - 1

x = \frac{- 5 - 7}{2 ( - 1 )} : 6

二次方程组的解是:

x = - 1, x = 6

作图

流行的例子

r^2-2r-4=2r^2+8

r^{2} - 2 r - 4 = 2 r^{2} + 8

r^{2} + 10 r + 16 = 0

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9 x^{2} + 5 x - 9 = 0

11x^2-13x=8x-3x^2

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