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?
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![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?](/uploads/image/z/1022516-44-6.jpg?t=%E5%B7%B2%E7%9F%A5P%3D7%2F15m-1%2CQ%3Dm%26sup2%3B-8%2F15m%28m%E4%B8%BA%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0%EF%BC%89%2C%E5%88%99P%E3%80%81Q%E7%9A%84%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E6%98%AF%3F)
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