设x1,x2是方程2x^2+4x-3=0的两个根,利用根与系数的关系,求下列各式的值.(1).(x1+3)(x2+3).(2).x2/x1+x1/x2.
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![设x1,x2是方程2x^2+4x-3=0的两个根,利用根与系数的关系,求下列各式的值.(1).(x1+3)(x2+3).(2).x2/x1+x1/x2.](/uploads/image/z/2082501-45-1.jpg?t=%E8%AE%BEx1%2Cx2%E6%98%AF%E6%96%B9%E7%A8%8B2x%5E2%2B4x-3%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%2C%E5%88%A9%E7%94%A8%E6%A0%B9%E4%B8%8E%E7%B3%BB%E6%95%B0%E7%9A%84%E5%85%B3%E7%B3%BB%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC.%EF%BC%881%EF%BC%89.%28x1%2B3%29%28x2%2B3%29.%EF%BC%882%EF%BC%89.x2%2Fx1%2Bx1%2Fx2.)
设x1,x2是方程2x^2+4x-3=0的两个根,利用根与系数的关系,求下列各式的值.(1).(x1+3)(x2+3).(2).x2/x1+x1/x2.
设x1,x2是方程2x^2+4x-3=0的两个根,利用根与系数的关系,求下列各式的值.
(1).(x1+3)(x2+3).(2).x2/x1+x1/x2.
设x1,x2是方程2x^2+4x-3=0的两个根,利用根与系数的关系,求下列各式的值.(1).(x1+3)(x2+3).(2).x2/x1+x1/x2.
x1,x2是方程2x^2+4x-3=0的两个根
由根与系数的关系得:x1+x2=-4/2=-2,x1*x2=-3/2
(1)(x1+3)(x2+3)=x1*x2+3(x1+x2)+9
=-3/2-6+9
=3/2
(2)通分之后有x1²+x2²出现,先算它
x1²+x2²=(x1+x2)²-2x1*x2
=4+3
=7
x2/x1+x1/x2=(x1²+x2²)/x1*x2=-14/3
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x1,x2是方程2x^2+4x-3=0的两个根
由韦达定理得:
x1+x2=-4/2=-2
x1x2=-3/2
(1))(x1+3)(x2+3)
=x1x2+3(x1+x2)+9
=-3/2-6+9
=3/2
(2)x2/x1+x1/x2
=(x1²+x2²)/(x1x2)
...
全部展开
x1,x2是方程2x^2+4x-3=0的两个根
由韦达定理得:
x1+x2=-4/2=-2
x1x2=-3/2
(1))(x1+3)(x2+3)
=x1x2+3(x1+x2)+9
=-3/2-6+9
=3/2
(2)x2/x1+x1/x2
=(x1²+x2²)/(x1x2)
=[(x1+x2)²-2x1x2]/(x1x2)
=(x1+x2)²/(x1x2)-2
=4/(-3/2)-2
=-8/3-2
=-14/3
收起
x1,x2是方程2x^2+4x-3=0的两个根
x1+x2=-2
x1*x2=-3/2
(x1+3)(x2+3)
=x1*x2+3(x1+x2)+9
=-3/2+3*(-2)+9
=-3/2-6+9
=3/2
x2/x1+x1/x2
=[(x1)^2+(x2)^2]/(x1*x2)
=[(x1)^2+(x2)^2+2x...
全部展开
x1,x2是方程2x^2+4x-3=0的两个根
x1+x2=-2
x1*x2=-3/2
(x1+3)(x2+3)
=x1*x2+3(x1+x2)+9
=-3/2+3*(-2)+9
=-3/2-6+9
=3/2
x2/x1+x1/x2
=[(x1)^2+(x2)^2]/(x1*x2)
=[(x1)^2+(x2)^2+2x1*x2-2x1*x2]/(x1*x2)
=[(x1+x2)^2-2x1*x2]/(x1*x2)
=[(-2)^2-2*(-3/2)]/(-3/2)
=(4+3)/(-3/2)
=-7*2/3
=-14/3
收起
x1+x2=-2
x1x2=-3/2
(1)(x1+3)(x2+3)
=x1x2+3(x1+x2)+9
=-3/2-6+9
=3/2
(2)x2/x1+x1/x2
=(x1²+x2²)/x1x2
=[(x1+x2)²-2x1x2]/x1x2
=[4+3]/(-3/2)
=-14/3
x1,x2是方程2x^2+4x-3=0的两个根
则x1+x2=-b/a=-2
x1x2=c/a=-3/2
则
(x1+3)(x2+3)=x1x2+3*(x1+x2)+9=-3/2+3*(-2)+9=3/2
x2/x1+x1/x2=(x2²+x1²)/x1x2=[(x1+x2)²-2x1x2]/x1x2=(x1+x2)²/x1x2-2=4/*(-3/2)-2=-14/3