设x1和x2是方程2x²-6x+3=0,求下列各式的值.x1²x2+x1x2² 1/x1-1/x2 x1-x2用韦达定理怎么变形?
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![设x1和x2是方程2x²-6x+3=0,求下列各式的值.x1²x2+x1x2² 1/x1-1/x2 x1-x2用韦达定理怎么变形?](/uploads/image/z/4478482-10-2.jpg?t=%E8%AE%BEx1%E5%92%8Cx2%E6%98%AF%E6%96%B9%E7%A8%8B2x%26%23178%3B-6x%2B3%3D0%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC.x1%26%23178%3Bx2%2Bx1x2%26%23178%3B+1%2Fx1-1%2Fx2+x1-x2%E7%94%A8%E9%9F%A6%E8%BE%BE%E5%AE%9A%E7%90%86%E6%80%8E%E4%B9%88%E5%8F%98%E5%BD%A2%EF%BC%9F)
设x1和x2是方程2x²-6x+3=0,求下列各式的值.x1²x2+x1x2² 1/x1-1/x2 x1-x2用韦达定理怎么变形?
设x1和x2是方程2x²-6x+3=0,求下列各式的值.
x1²x2+x1x2² 1/x1-1/x2
x1-x2用韦达定理怎么变形?
设x1和x2是方程2x²-6x+3=0,求下列各式的值.x1²x2+x1x2² 1/x1-1/x2 x1-x2用韦达定理怎么变形?
∵x1,x2是方程的·两个根
∴x1x2=c/a=-3/2
x1+x2=-b/a=3
(1)x1x2(x1+x2)
=-3/2*3
=-9/2
(2)1/x1-1/x2=(x2-x1)/x1x2
=√(x2+x1)²-4x1x2/x1x2
=√9+6/(-3/2)
=√15/(-3/2)
=-2√15/2或2√15/2
x1+x2=6/2=3
x1x2=3/2
x1^2x2+x1x2^2
=(x1x2)(x1+x2)
=3*3/2
=9/2
1/x1-1/x2=(x2-x1)/x1x2=2(x2-x1)/3
(x1-x2)^2=x1^2-2x1x2+x2^2
=(x1+x2)^2-4x1x2
=9-4*3/2
=3
1/x1-1/x2=±2√3/3