已知实数a、b满足ab=1,M=a/a+1+b/b+1,N=1/a+1+1/b+1

Question

已知实数a、b满足ab=1,M=a/a+1+b/b+1,N=1/a+1+1/b+1

Answer 1

已知实数a、b满足ab=1,M=a/(a+1)+b/(b+1),N=1/(a+1)+1/(b+1),判断M与N的大小
M-N=[a/(a+1)+b/(b+1)]-[1/(a+1)+1/(b+1)]
=[(a(b+1)+b(a+1)]/(a+1)(b+1)-[(b+1)+(a+1)]/(a+1)(b+1)
=[(2ab+a+b)-(a+b+2)]/(a+1)(b+1)
=(2ab-2)/(a+1)(b+1)=(2-2)/(a+1)(b+1)=0
故M=N.
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