已知a,b为实数,且ab=1,设M=a/a+1+b/b+1,N=1/a+1+1/b+1,试比较M,N的大小关系,做出猜想并验证

问题描述:

已知a,b为实数,且ab=1,设M=a/a+1+b/b+1,N=1/a+1+1/b+1,试比较M,N的大小关系,做出猜想并验证

∵a·b=1∴M=a/﹙a+1﹚+b/﹙b+1﹚=a/﹙a+ab﹚+b/﹙b+ab﹚=a/a﹙b+1﹚+b/b﹙a+1﹚=1/﹙a+1﹚+1/﹙b+1﹚=N∴ M=N.或M - N = a/(a + 1)+ b/(b + 1)- 1/(a + 1)- 1/(b + 1)=(a - 1)/(a + ...