过点A作BC边的垂线,垂足为点Q,
则BQ=CQ
(1)若P与Q重合,则AP^2+PB*PC=AP^2+BQ^2=AB^2=5^2=25
(2)若P与Q不重合,则
PB=BQ+PQ,PC=CQ-PQ=BQ-PQ
PB*PC=(BQ+PQ)*(BQ-PQ)=BQ^2-PQ^2
AP^2=AQ^2+PQ^2
所以
AP＾2＋PB*PC=AQ^2+PQ^2+BQ^2-PQ^2=AB^2=5^2=25