用因式分解解下列方程: (1)(2x-1)(3x+4)=2x-1; (2)3(x-3)=(x-3)2; (3)(2x+3)2=24x; (4)1.2x-0.04=9x2.
问题描述:
用因式分解解下列方程:
(1)(2x-1)(3x+4)=2x-1;
(2)3(x-3)=(x-3)2;
(3)(2x+3)2=24x;
(4)1.2x-0.04=9x2.
答
(1)方程变形得:(2x-1)(3x+4)-(2x-1)=0,
分解因式得:(2x-1)(3x+4-1)=0,
解得:x1=
,x2=-1;1 2
(2)方程变形得:3(x-3)-(x-3)2=0,
分解因式得:(x-3)(3-x+3)=0,
解得:x1=0,x2=3;
(3)方程整理得:4x2-12x+9=0,即(2x-3)2=0,
解得:x1=x2=1.5;
(4)方程变形得:900x2-120x+4=0,即(30x-2)2=0,
解得:x1=x2=
.1 15