Question

如图,已知抛物线y=x方-6x+5与x轴相交于点A、B,点P是抛物线上一点,且三角形abp面积为8,则p的坐标为

Answer 1

x²-6x+5=0

(x-1)(x-5)=0

x=1或x=5

线段AB的长度为5-1=4

设p坐标为(m,n)

n=±8×2÷4=±4

①n=4

m²-6m+5=4

m²-6m+1=0

△=36-4=32

m=(6±4√2)/2=3±2√2

③n=-4

m²-6m+5=-4

m²-6m+9=0

(m-3)²=0

m=3

综上,p坐标有三个,分别是

(3+2√2,4)(3-2√2,4),(3,-4)