已知实数a、b满足ab=1那么1/(a^2+1)+1/(b^2+1)的值为

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/24 08:42:59
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

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