已知实数a、b满足ab=1,求(a²+1/1)+(b²+1/1)的值

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已知实数a、b满足ab=1,求(a²+1/1)+(b²+1/1)的值

已知实数a、b满足ab=1,求(a²+1/1)+(b²+1/1)的值
已知实数a、b满足ab=1,求(a²+1/1)+(b²+1/1)的值

已知实数a、b满足ab=1,求(a²+1/1)+(b²+1/1)的值
1/(a^2+1)+1/(b^2+1)
=(b^2+1+a^2+1)/(a^2+1)(b^2+1)
=(a^2+b^2+2)/(a^2b^2+a^2+b^2+1)
=(a^2+b^2+2)/(1+a^2+b^2+1)
=1