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阅读材料:∵ax2+bx+c=0(a≠0)有两根为..∴,.综上得,设ax2+bx+c=0...
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阅读材料:∵ax
2+bx+c=0(a≠0)有两根为
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAAAsCAYAAABi4kbYAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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==
)
.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAAAsCAYAAABi4kbYAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
.∴
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHgAAAAjCAYAAABfLc7mAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAAAxCAYAAADJEws5AAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
.综上得,设ax
2+bx+c=0(a≠0)的两根为x
1、x
2,则有
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE0AAAAjCAYAAADR94eaAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAAjCAYAAAAqoHJFAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
.利用此知识解决:已知x
1,x
2是方程x
2-x-1=0的两根,不解方程求下列式子的值:
①x
12+x
22;
②(x
1+1)(x
2+1).
相关试题
-
阅读下面的材料:
ax2+bx+c=0(a≠0)的根为,
.
∴
,
.
综上所述得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有:
.
请利用这一结论解决下列问题:
(1)若x2+bx+c=0的两根为1和3,求b和c的值.
(2)设方程2x2+3x+1=0的根为x1、x2,求x12+x12的值.
-
阅读下面的材料:
ax2+bx+c=0(a≠0)的根为,
.
∴
,
.
综上所述得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有:
.
请利用这一结论解决下列问题:
(1)若x2+bx+c=0的两根为1和3,求b和c的值.
(2)设方程2x2+3x+1=0的根为x1、x2,求x12+x12的值.
-
阅读下面的材料:
ax2+bx+c=0(a≠0)的根为,
.
∴
,
.
综上所述得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有:
.
请利用这一结论解决下列问题:
(1)若x2+bx+c=0的两根为1和3,求b和c的值.
(2)设方程2x2+3x+1=0的根为x1、x2,求x12+x12的值.
-
阅读下面的材料:
ax2+bx+c=0(a≠0)的根为,
.
∴
,
.
综上所述得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有:
.
请利用这一结论解决下列问题:
(1)若x2+bx+c=0的两根为1和3,求b和c的值.
(2)设方程2x2+3x+1=0的根为x1、x2,求x12+x12的值.
-
阅读下面的材料:
ax2+bx+c=0(a≠0)的根为,
.
∴
,
.
综上所述得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有:
.
请利用这一结论解决下列问题:
(1)若x2+bx+c=0的两根为1和3,求b和c的值.
(2)设方程2x2+3x+1=0的根为x1、x2,求x12+x12的值.
-
阅读下面的材料:
ax2+bx+c=0(a≠0)的根为,
.
∴
,
.
综上所述得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有:
.
请利用这一结论解决下列问题:
(1)若x2+bx+c=0的两根为1和3,求b和c的值.
(2)设方程2x2+3x+1=0的根为x1、x2,求x12+x12的值.
-
阅读材料:∵ax2+bx+c=0(a≠0)有两根为
.
.∴
,
.综上得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有
,
.利用此知识解决:
(1)已知x1,x2是方程x2-x-1=0的两根,不解方程求下列式子的值:①x12+x22;②(x1+1)(x2+1);
(2)是否存在实数m,使关于x的方程x2+(m+1)x+m+4=0的两根平方和等于2?若存在,求出满足条件的m的值;若不存在,说明理由.
-
阅读材料:∵ax2+bx+c=0(a≠0)有两根为
.
.∴
,
.综上得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有
,
.利用此知识解决:
(1)已知x1,x2是方程x2-x-1=0的两根,不解方程求下列式子的值:①x12+x22;②(x1+1)(x2+1);
(2)是否存在实数m,使关于x的方程x2+(m+1)x+m+4=0的两根平方和等于2?若存在,求出满足条件的m的值;若不存在,说明理由.
-
阅读材料:∵ax2+bx+c=0(a≠0)有两根为
.
.∴
,
.综上得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有
,
.利用此知识解决:
(1)已知x1,x2是方程x2-x-1=0的两根,不解方程求下列式子的值:①x12+x22;②(x1+1)(x2+1);
(2)是否存在实数m,使关于x的方程x2+(m+1)x+m+4=0的两根平方和等于2?若存在,求出满足条件的m的值;若不存在,说明理由.
-
阅读材料:∵ax2+bx+c=0(a≠0)有两根为
.
.∴
,
.综上得,设ax2+bx+c=0(a≠0)的两根为x1、x2,则有
,
.利用此知识解决:已知x1,x2是方程x2-x-1=0的两根,不解方程求下列式子的值:
①x12+x22;
②(x1+1)(x2+1).