已知抛物线y=x²+kx-k为常数,且k>0)抛物线与x轴交MN两点,则两点之间的距离为MN= (用含k的式子表示)
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![已知抛物线y=x²+kx-k为常数,且k>0)抛物线与x轴交MN两点,则两点之间的距离为MN= (用含k的式子表示)](/uploads/image/z/5304350-38-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dx%26%23178%3B%2Bkx-k%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E4%B8%94k%3E0%29%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8Ex%E8%BD%B4%E4%BA%A4MN%E4%B8%A4%E7%82%B9%2C%E5%88%99%E4%B8%A4%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BAMN%3D+%EF%BC%88%E7%94%A8%E5%90%ABk%E7%9A%84%E5%BC%8F%E5%AD%90%E8%A1%A8%E7%A4%BA%EF%BC%89)
已知抛物线y=x²+kx-k为常数,且k>0)抛物线与x轴交MN两点,则两点之间的距离为MN= (用含k的式子表示)
已知抛物线y=x²+kx-k为常数,且k>0)抛物线与x轴交MN两点,则两点之间的距离为MN= (用含k的式子表示)
已知抛物线y=x²+kx-k为常数,且k>0)抛物线与x轴交MN两点,则两点之间的距离为MN= (用含k的式子表示)
令y=0,得:
x²+kx-k=0
x1+x2=-k,x1*x2=-k
MN=|x1-x2|=√(x1-x2)²
=√[(x1+x2)²-4x1*x2]
=√(k²+4k)