已知P=7/15m-1,Q=m²-8/15m(m为任意实数）,则P、Q的大小关系是?

已知P=7/15m-1,Q=m²-8/15m(m为任意实数）,则P、Q的大小关系是?
已知P=7/15m-1,Q=m²-8/15m(m为任意实数）,则P、Q的大小关系是?

已知P=7/15m-1,Q=m²-8/15m(m为任意实数）,则P、Q的大小关系是?
P-Q=7/15m-1-(m²-8/15m)
=7/15m-1-m²+8/15m
=-m²+m-1
=-(m²-m+1/4)-1+1/4
=-(m-1/2)²-3/4

Q-P
=m²-8/15m-7/15m+1
=m²-m+1/4+3/4
=(m-1/2)²+3/4≥3/4＞0
所以Q>P

Q-P=m^2-m+1=(m-1/2)^2+3/4>0
所以Q>P