a、b为实数,且ab=1,设P=(a/a+1)+(b/b+1),Q=(1/a+1)+(1/b+1),则PQ关系是?(>.
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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PQ关系是?(>.](/uploads/image/z/3726537-33-7.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%2B1%29%2B%28b%2Fb%2B1%29%2CQ%3D%281%2Fa%2B1%29%2B%281%2Fb%2B1%29%2C%E5%88%99PQ%E5%85%B3%E7%B3%BB%E6%98%AF%3F%EF%BC%88%3E.)
a、b为实数,且ab=1,设P=(a/a+1)+(b/b+1),Q=(1/a+1)+(1/b+1),则PQ关系是?(>.
a、b为实数,且ab=1,设P=(a/a+1)+(b/b+1),Q=(1/a+1)+(1/b+1),则PQ关系是?(>.
a、b为实数,且ab=1,设P=(a/a+1)+(b/b+1),Q=(1/a+1)+(1/b+1),则PQ关系是?(>.
P=(a/a+1)+(b/b+1)
=(a(b+1)/(a+1)(b+1))+(b(a+1)/(a+1)(b+1))
=((ab+a)/(a+1)(b+1))+((ab+b)/(a+1)(b+1))
=((1+a)/(a+1)(b+1))+((1+b)/(a+1)(b+1))
=(1/(b+1))+(1/(a+1))=Q
所以P=Q
通分一下就做出来了.
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因为ab=1,
所以P=a/(a+1)+b/(b+1)
=a/(a+1)+ab/(ab+a)
=a/(a+1)+1/(1+a)
=(a+1)/(a+1)
=1,
Q=1/(a+1)+1/(b+1)
=1/(a+1)+a/(ab+a)
=1/(a+1)+a/(1+a)
=(1+a)/(a+1)
=1,
所以P=Q...
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因为ab=1,
所以P=a/(a+1)+b/(b+1)
=a/(a+1)+ab/(ab+a)
=a/(a+1)+1/(1+a)
=(a+1)/(a+1)
=1,
Q=1/(a+1)+1/(b+1)
=1/(a+1)+a/(ab+a)
=1/(a+1)+a/(1+a)
=(1+a)/(a+1)
=1,
所以P=Q
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