已知实数a,b满足ab=1,求1/(a²+1)+1/(b²+1)的值
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已知实数a,b满足ab=1,求1/(a²+1)+1/(b²+1)的值
已知实数a,b满足ab=1,求1/(a²+1)+1/(b²+1)的值
已知实数a,b满足ab=1,求1/(a²+1)+1/(b²+1)的值
ab=1,
1/(a²+1)+1/(b²+1)
=(b²+1)/(a²+1)(b²+1)+(a²+1)/(b²+1)(a²+1)
=(a²+1+1+b²+1)/(a²+1)(b²+1)
=(a²+2+b²)/(a²b²+a²+b²+1)
=(a²+2+b²)/(1+a²+b²+1)
=1
因为ab=1则1/(a²+1)+1/(b²+1)=ab/(a²+ab)+ab/(b²+ab)=(分别约掉a,b)b/(a+b)+a/(b+a)=(a+b)/(a+b)=1
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