按要求解下列方程(1)x 2 -2x-4=0(公式法)(2)2x 2 -3x-5=0(配方法)(3)(x+1)(x+8)=-12(4)3

2024-12-12 09:36:57
推荐回答(1个)
回答1:

(1)∵一元二次方程x 2 -2x-4=0中,a=1,b=-2,c=-4,
∴x=
(-2 ) 2 -4×1×(-4)
2×1
=
2±2
5
2
=1±
5

∴x 1 =1+
5
,x 2 =1-
5


(2)∵原方程可化为2(x 2 -
3
2
x-
5
2
)=0,
配方得,2[x 2 -
3
2
x+(
3
4
2 -(
3
4
2 -
5
2
]=0,即2[(x-
3
4
2 -
49
16
]=0,
∴(x-
3
4
2 =
49
16

∴x-
3
4
7
4
,即x 1 =
5
2
,x 2 =-1;

(3)∵原方程可化为:x 2 +9x+20=0,
∴x=
-9±
81-4×20
2
=
-9±1
2

∴x 1 =-4,x 2 =-5;

(4)∵原方程可化为3(x-5) 2 +x(x-5)=0,
提取公因式得,(x-5)(4x-15)=0,
∴x-5=0,4x-15=0,
解得x 1 =5,x 2 =
15
4