题目内容
用适当方法解下列方程:
(1)2x2-5x-3=0
(2)(2x-3)2-2(2x-3)-3=0
(3)(2x-1)2=9
(4)3x2+5(2x+1)=0.
(1)2x2-5x-3=0
(2)(2x-3)2-2(2x-3)-3=0
(3)(2x-1)2=9
(4)3x2+5(2x+1)=0.
(1)因式分解得(x-3)(2x+1)=0,
即x-3=0或2x+1=0,
解得x1=3,x2=-
;
(2)设2x-3=t,则方程即可变形为t2-2t-3=0,
(t+1)(t-3)=0,
解得t=-1或3,
即2x-3=-1或3,
解得x1=1,x2=3;
(3)开平方,得2x-1=±3,
解得x1=2,x2=-1;
(4)整理得3x2+10x+5=0,
∵a=3,b=10,c=5,△=b2-4ac=100-60=40,
∴x=
=
=
,
∴x1=
,x2=
.
即x-3=0或2x+1=0,
解得x1=3,x2=-
1 |
2 |
(2)设2x-3=t,则方程即可变形为t2-2t-3=0,
(t+1)(t-3)=0,
解得t=-1或3,
即2x-3=-1或3,
解得x1=1,x2=3;
(3)开平方,得2x-1=±3,
解得x1=2,x2=-1;
(4)整理得3x2+10x+5=0,
∵a=3,b=10,c=5,△=b2-4ac=100-60=40,
∴x=
-b±
| ||
2a |
-10±
| ||
6 |
-5±
| ||
3 |
∴x1=
-5+
| ||
3 |
-5-
| ||
3 |
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