小专题一一元二次方程的解法

1、v1.0可编辑可修改专题(一)一元二次方程的解法62 27= 0;2(3)(x - 2) = 9;(4)(2y23) = 16.1 用直接开平方法解下列方程：(1) x (4) 2x + 7x + 3 = 0.- 16= 0;(2)3x2 .用配方法解下列方程:(1) x 2- 4x 1 = 0;(2) 2x 2 4x 8 = 0;2(3) 3x 6x + 4 = 0;3 用公式法解下列方程：(1) x (2) (x 3) 9 = 0;- 2 3x + 3= 0;2(2) 3x + 5x + 2 = 0;2(3) 4x + 3x 2 = 0;(4) 3x =2(x + 1)(x 1) 4 .用

2、因式分解法解下列方程:2(1) x 3x = 0;2(3x - 2) + (2 -3x) = 0;2(4)2(t - 1) + 8t = 0;2(5) 3x + 15=- 2x - 10x;2(6) x - 3x = (2 - x)(x - 3).5.用合适的方法解下列方程：2 2(1) 4(x - 3) - 25(x - 2) = 0;2 2(2) 5(x - 3) = x - 9;2(3)t1+ 8= °参考答案1. (1)移项，得x = 16,根据平方根的定义，得x =± 4, 即卩X1 = 4, X2= 4. 移项，得3x? = 27,两边同除以3,得X = 9,根

3、据平方根的定义，得x =± 3,即X1 = 3, X2= 3.(3) 根据平方根的定义，得x 2=± 3,即Xi = 5, X2= 1. 根据平方根的定义，得2y 3=± 4,即y1 = j, ¥ = 1.2. (1)移项，得 x2 4x = 1.配方，得 x2 4x+ 22= 1 + 4,即(x 2)2= 5.直接开平方，得 x 2=± ,；5,. X1 = 2+ ,；5,移项，得2x2 4x= 8.两边都除以2,得X2 = 2 飞:5x2 2x = 4.配方，得 X2 2x+ 1= 4+ 1. / (X 1)2= 5. .x 1 =

4、77; ；5.xi= 1 + '5, X2= 1 一、： 5X2 2x = 4.配方,1,得 移项，得3x2 6x= 4.二次项系数化为4122r22I得 x 2x + 1 = 3+ 1，即(X 1) = 3实数的平方不可能是负数，.原方程无实数根.(4)移项，得2x2+ 7x= 3.方程两边同除以2,得273X + ?X= 2 配方,277 237 27 2得 x + 2X + (4) = 2+(4)，即(x + 4)=25.直接开平方，得 x + 7 =± 4.X1= 2, X2= 3.2X13. (1) v a= 1, b = 2 3, c = 3, b 4ac= (

5、2 3)2 4X 1 X 3= 0, . x = = a： 3.X1 = X2 = ' 3(2) 方程的两边同乘1，得 3x2 5x 2= 0. v a= 3, b= 5, c = 2, b24ac = ( 5)2 4X 3X ( 2) = 49>0,2X3. x=-(- 5)±畅=空.X1= 2, X2= 13a = 4, b= 3, c= 4ac = 3 4X4X ( 2) = 41> =2X488(4) 将原方程化为一般形式，得 ： 2x I.： 3x '：. 2 = 0. v a=打 2 , b= ：. 3 , c= 2, b 4ac = ( 3)

6、 4X %、2 X (2) = 11>0 , x= 32±= V. X1=? , X2 = 4. (1)x(x 3) = 0，二 x = 0 或 x 3 = 0,.Xi= 0, X2= 3.2 2(2) T (x - 3) - 3 = 0 , (x - 3+ 3)(x - 3- 3) = 0. / x(x - 6) = 0. / x= 0 或 x - 6 = 0. /-x 1= 0, X2= 6.2 2(3) 原方程可化为(3x - 2)2- (3x - 2) = 0,/ (3x - 2)(3x - 2 - 1) = 0. 3x- 2 = 0 或 3x- 3 = 0,/ Xi=

7、 - , X2= 1.3222(4) 原方程可化为 2t + 4t + 2= 0. /t - 2t + 1 = 0. (t - 1) = 0,/ ti= t2= 1.2(5) 移项，得 3x + 15+ (2x + 10x) = 0,/ 3(x + 5) + 2x(x + 5) = 0,即(x + 5)(3 + 2x) = 0. x+ 5= 0 或 3+ 2x =30.X1 = 5, X2=.2(6) 原方程可化为 x(x 3) = (2 x)(x 3) 移项，得 x(x 3) (2 x)(x 肝一3) = 0. (x 3)(2x 2) = 0. / x 3 =0 或 2x 2 = 0. /-

8、x 1 = 3, X2= 1.22225. (1)变形为2(x - 3) - 5(x - 2) = 0,即(2x - 6) - (5x - 10) = 0. / (2x - 6 + 5x- 10)(2x - 6- 5x + 10) = 0,即164(7x 16)( 3x + 4) = 0. -x 1 = , X2 = 3.732 2(2) 5(x . - 3) = (x + 3)(x - 3),整理得 5(x - 3)一 (x + 3)(x - 3) = 0. / (x - 3)5(x - 3) - (x + 3) = 0，即(x - 3)(4x9-18) = 0. / x- 3= 0 或 4x 18 = 0.(3) 方程两边都乘以 8，得 8t2 -