Question

The sum of the reciprocals of two consecutive integers is startfraction 11 over 30 endfraction 11 30. find the two integers.

Answer 1

$\dfrac{1}{n}+\dfrac{1}{n+1}=\dfrac{11}{30}\\ 30n+30(n+1)=11n(n+1)\\ 30n+30n+30=11n^2+11n\\ 11n^2-49n-30=0\\ 11n^2-55n+6n-30=0\\ 11n(n-5)+6(n-5)=0\\ (11n+6)(n-5)=0\\ n=-\dfrac{6}{11} \vee n=5\\\\n=5,n+1=6$

It's 5 and 6.