设x1,x2是方程2x²+4x+-3=0的两个根不解方程求下列各式的值 1.(x1+1)(x2+1) 2.x2/x1+x1/x2在线等我很着急.
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![设x1,x2是方程2x²+4x+-3=0的两个根不解方程求下列各式的值 1.(x1+1)(x2+1) 2.x2/x1+x1/x2在线等我很着急.](/uploads/image/z/2541319-7-9.jpg?t=%E8%AE%BEx1%2Cx2%E6%98%AF%E6%96%B9%E7%A8%8B2x%26%23178%3B%2B4x%2B-3%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%E4%B8%8D%E8%A7%A3%E6%96%B9%E7%A8%8B%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC+1.%28x1%2B1%29%28x2%2B1%29+2.x2%EF%BC%8Fx1%2Bx1%EF%BC%8Fx2%E5%9C%A8%E7%BA%BF%E7%AD%89%E6%88%91%E5%BE%88%E7%9D%80%E6%80%A5.)
设x1,x2是方程2x²+4x+-3=0的两个根不解方程求下列各式的值 1.(x1+1)(x2+1) 2.x2/x1+x1/x2在线等我很着急.
设x1,x2是方程2x²+4x+-3=0的两个根不解方程求下列各式的值 1.(x1+1)(x2+1) 2.x2/x1+x1/x2
在线等我很着急.
设x1,x2是方程2x²+4x+-3=0的两个根不解方程求下列各式的值 1.(x1+1)(x2+1) 2.x2/x1+x1/x2在线等我很着急.
是-3吧?
x1+x2=-2
x1x2=-3/2
所以
(x1+1)(x2+1)
=x1x2+(x1+x2)+1
=-3/2-2+1
=-5/2
x1+x2=-2
两边平方
x1²+2x1x2+x2²=4
x1²+x2²=4-2x1x2=7
所以x2/x1+x1/x2
=(x2²+x1²)/x1x2
=7/(-3/2)
=-14/3
解由题知x1+x2=-2,x1x2=-3/2
故1(x1+1)(x2+1)
=x1x2+(x1+x2)+1
=-3/2-2+1
=-5/2
2 x2/x1+x1/x2
=(x2^2+x1^2)/x1x2
=[(x1+x2)^2-2x1x2]/x1x2
=[(x1+x2)^2]/x1x2-2
=(-2)^2/(-3/2)-2
=-8/3-2
=-14/3.
2x^2+4x-3=0
x1+x2=-2 x1x2=-3/2
(x1+1)(x2+1)=x1x2+x1+x2+1=-3/2-2+1=-5/2
x2/x1+x1/x2=(x1^2+x2^2)/x1x2=[(x1+x2)^2-2x1x2]/x1x2=-14/3
根据韦达定理有
x1+x2=-b/a=-4/2=-2
x1*x2=c/a=-3/2,则有
1、
(x1+1)(x2+1)
=x1*x2+x1+x2+1
=-3/2-2+1
=-5/2
2、
x2/x1+x1/x2
=(X2^2+x1^2)/x1*x2
=[(x1+x2)^2-2x1*x2]/x1*x2
=(4+3)/-3/2=-14/3