已知实数a、b满足ab=1那么1/(a^2+1)+1/(b^2+1)的值为

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已知实数a、b满足ab=1那么1/(a^2+1)+1/(b^2+1)的值为
已知实数a、b满足ab=1那么1/(a^2+1)+1/(b^2+1)的值为

已知实数a、b满足ab=1那么1/(a^2+1)+1/(b^2+1)的值为
1/(a^2+1)+1/(b^2+1)
=a^2+b^2+2/a^2×b^2+a^2+b^2+1
因为ab=1
所以a^2×b^2=(ab)^2=1
原式=a^2+b^2+2/a^2+b^2
=1

1


ab=1
1/(a^2+1)+1/(b^2+1)
=ab/(a^2+ab)+ab/(b^2+ab)
=b/(a+b)+a/(a+b)
=(a+b)/(a+b)
=1


ab=1
1/(a^2+1)+1/(b^2+1)
=ab/(a^2+ab)+ab/(b^2+ab)
=b/(a+b)+a/(a+b)
=(a+b)/(a+b)
=1