a、b为实数,且ab=1,设P=(a/a-1)+(b/b-1),Q=(1/a-1)+(1/b-1),则P()Q?
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![a、b为实数,且ab=1,设P=(a/a-1)+(b/b-1),Q=(1/a-1)+(1/b-1),则P()Q?](/uploads/image/z/3726538-34-8.jpg?t=a%E3%80%81b%E4%B8%BA%E5%AE%9E%E6%95%B0%2C%E4%B8%94ab%3D1%2C%E8%AE%BEP%3D%28a%2Fa-1%29%2B%28b%2Fb-1%29%2CQ%3D%281%2Fa-1%29%2B%281%2Fb-1%29%2C%E5%88%99P%EF%BC%88%EF%BC%89Q%3F)
a、b为实数,且ab=1,设P=(a/a-1)+(b/b-1),Q=(1/a-1)+(1/b-1),则P()Q?
a、b为实数,且ab=1,设P=(a/a-1)+(b/b-1),Q=(1/a-1)+(1/b-1),则P(<,=或>)Q?
a、b为实数,且ab=1,设P=(a/a-1)+(b/b-1),Q=(1/a-1)+(1/b-1),则P()Q?
P=a/(a-1)+b/(b-1),Q=1/(a-1)+1/(b-1)
∴P-Q
=a/(a-1)-1/(a-1)+b/(b-1)-1/(b-1)
=(a-1)/(a-1)+(b-1)/(b-1)
=2>0
∴P>Q
P-Q=(a/a-1)+(b/b-1)-(1/a-1)+(1/b-1)=(a-1)/(a-1)+(b-1)/(b-1)=2>0
P>Q