解下列方程(1)(2x+3) 2 -25=0.(直接开平方法)(2) 2x 2 -7x-2=0(公式法)(3)(x+2) 2 =3(x+

2024-11-22 12:00:22
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回答1:

(1)(2x+3) 2 -25=0,
移项得,(2x+3) 2 =25,
∴2x+3=5或2x+3=-5,
解得:x 1 =1,x 2 =-4;

(2) 2x 2 -7x-2=0,
a=2,b=-7,c=-2,
△=b 2 -4ac=49+16=65,
x=
65
2×2
=
65
4

所以 x 1 =
7+
65
4
x 2 =
7-
65
4


(3)(x+2) 2 =3(x+2),
移项得,(x+2) 2 -3(x+2)=0,
因式分解得,(x+2)[(x+2)-3]=0,
解得:x 1 =-2,x 2 =1;

(4)2x 2 +x-6=0,
因式分解得,(2x-3)(x+2)=0,
∴2x-3=0,x+2=0,
解得:x 1 =
3
2
,x 2 =-2.