已知抛物线:y=x^2+kx-3/4k^2 设抛物线与x轴交与m.n,若这两点到原点的距离分别是OM,ON,且1/ON-1/OM=2/3求
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![已知抛物线:y=x^2+kx-3/4k^2 设抛物线与x轴交与m.n,若这两点到原点的距离分别是OM,ON,且1/ON-1/OM=2/3求](/uploads/image/z/11698763-59-3.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BF%3Ay%3Dx%5E2%2Bkx-3%2F4k%5E2+%E8%AE%BE%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%B8%8Em.n%2C%E8%8B%A5%E8%BF%99%E4%B8%A4%E7%82%B9%E5%88%B0%E5%8E%9F%E7%82%B9%E7%9A%84%E8%B7%9D%E7%A6%BB%E5%88%86%E5%88%AB%E6%98%AFOM%2CON%2C%E4%B8%941%2FON-1%2FOM%3D2%2F3%E6%B1%82)
已知抛物线:y=x^2+kx-3/4k^2 设抛物线与x轴交与m.n,若这两点到原点的距离分别是OM,ON,且1/ON-1/OM=2/3求
已知抛物线:y=x^2+kx-3/4k^2 设抛物线与x轴交与m.n,若这两点到原点的距离分别是OM,ON,且1/ON-1/OM=2/3求
已知抛物线:y=x^2+kx-3/4k^2 设抛物线与x轴交与m.n,若这两点到原点的距离分别是OM,ON,且1/ON-1/OM=2/3求
y=x^2+kx-3/4k^2=(x-3/2k)(x+1/2k)
x1=3/2k
x2=-1/2k
因为k>0
所以OM=3/2k,ON=1/2k
代入1/ON-1/OM=2/3得k=2
设:x^2+kx-3k^2/4=0
则:x1+x2=-k,x1x2=-3k^2/4
(x1-x2)^2=(x1+x2)^2-4x1x2=k^2+3k^2=4k^2
x1-x2=|2k|
1/ON-1/OM
=(OM-ON)/ON*OM
=(x1-x2)/x1x2
=|2k|/(-3k^2/4)
=8/3|k|
=2/3
k=±4