相关试题
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小红、小亮两位同学一起解方程x(2x-5)+4(5-2x)=0.小红是这样解的:先将方程变为x(2x-5)-4(2x-5)=0,移向得x(2x-5)=4(2x-5),方程两边都除以(2x-5)得x=4,小亮看后说小红的解法不对,请你判断小红的解法是否正确?若不正确,请给出正确解法及答案.
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解方程:
(1)用配方法解方程:x2+2x-1=0
(2)用公式法解方程:2x2+x-6=0
(3)用因式分解法解方程:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAAZCAYAAADUicu/AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
(4)选择一种自己喜欢的方法解方程:(2x-1)2=x2+2x+1.
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(2004•黄冈)下列说法中正确的是( )
A.方程x2+2x-7=0的两实数根之和是2
B.方程2x2-3x-5=0的两实数根之积为![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAC9SURBVDhPvVPbDcQwCGMydmKdLMMoGYWDvA7S
NPmJWimqFLm2wS7I4YF7gJxQAKAeTJIbdZNgIXfpZSuASYjXbhSQJWGjBpIZF6ZgMiBK6gaU9DFm
Mev0FnuIhteAHQPT7CEnwb4gfc/jXsziLdWzxEjQGe13xnpmuNQo7cOqTdWDbXKsT4Mysz6LzDz6
Z1+UuJ+ddFZNbp9mDCzuIfiprA5g5d2Udi5Kd1UYzHkoivtPoFZ9Pn+pz8LaZP4D24Hl+DyU7CsA
AAAASUVORK5CYII=
)
C.方程x2-2x-7=0的两实数根的平方和为-18
D.方程2x2+3x-5=0的两实数根的倒数和为
-
(2004•黄冈)下列说法中正确的是( )
A.方程x2+2x-7=0的两实数根之和是2
B.方程2x2-3x-5=0的两实数根之积为![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAC9SURBVDhPvVPbDcQwCGMydmKdLMMoGYWDvA7S
NPmJWimqFLm2wS7I4YF7gJxQAKAeTJIbdZNgIXfpZSuASYjXbhSQJWGjBpIZF6ZgMiBK6gaU9DFm
Mev0FnuIhteAHQPT7CEnwb4gfc/jXsziLdWzxEjQGe13xnpmuNQo7cOqTdWDbXKsT4Mysz6LzDz6
Z1+UuJ+ddFZNbp9mDCzuIfiprA5g5d2Udi5Kd1UYzHkoivtPoFZ9Pn+pz8LaZP4D24Hl+DyU7CsA
AAAASUVORK5CYII=
)
C.方程x2-2x-7=0的两实数根的平方和为-18
D.方程2x2+3x-5=0的两实数根的倒数和为
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观察下列方程:
①2x2-27x+91=0;②2x2-23x+66=0;③2x2-19x+45=0;④2x2-15x+28=0;⑤2x2-11x+15=0;…
上面每一个方程的二次项系数都是2,各个方程的解都不同,但每个方程b2-4ac的值均1.
(1)请你写出两个方程,使每个方程的二次项系数都是2,且每个方程的b2-4ac的值也都是1,但每个方程的解与已知的5个方程的解都不相同.
(2)对于一般形式的一元二次方程ax2+bx+c=0(a≠0,b2-4ac≥0),能否作出一个新方程ax2+b′x+c′=0,使b2-4ac与b′2-4ac′相等?若能,请写出所作的新的方程(b′,c′需用a,b,c表示),并说明理由;若不能,也请说明理由.
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下列四个说法中,正确的是( )
A.一元二次方程x2+2x+3=
有实数根
B.一元二次方程x2+2x+3=
有实数根
C.一元二次方程x2+2x+3=
有实数根
D.一元二次方程x2+2x+3=2a(a≥1)有实数根
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下列方程中,两实数根的和等于2的方程是( )
A.2x2-4x+3=0
B.2x2-2x-3=0
C.2x2+4x+3=0
D.2x2-4x-3=0
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下列说法中正确的是( )
A.方程x2+2x-7=0的两实数根之和是2
B.方程2x2-3x-5=0的两实数根之积为![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAC9SURBVDhPvVPbDcQwCGMydmKdLMMoGYWDvA7S
NPmJWimqFLm2wS7I4YF7gJxQAKAeTJIbdZNgIXfpZSuASYjXbhSQJWGjBpIZF6ZgMiBK6gaU9DFm
Mev0FnuIhteAHQPT7CEnwb4gfc/jXsziLdWzxEjQGe13xnpmuNQo7cOqTdWDbXKsT4Mysz6LzDz6
Z1+UuJ+ddFZNbp9mDCzuIfiprA5g5d2Udi5Kd1UYzHkoivtPoFZ9Pn+pz8LaZP4D24Hl+DyU7CsA
AAAASUVORK5CYII=
)
C.方程x2-2x-7=0的两实数根的平方和为-18
D.方程2x2+3x-5=0的两实数根的倒数和为
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解下列方程
(1)用公式法解方程:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAZCAYAAABXTfKEAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
(2)用配方法解方程:2x2+2
x+1=0
(3)用因式分解法:(2y+1)2=4y+2
(4)用适当的方法解方程:x2-6x+9=(5-2x)2.
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(2000•山东)下列方程中,两实数根的和等于2的方程是( )
A.2x2-4x+3=0
B.2x2-2x-3=0
C.2x2+4x+3=0
D.2x2-4x-3=0