A scientist wants to research the potential spread of germs by contact. She knows that the number of possible handshakes within a group of n people is given by the equation Nequalsone half left parenthesis n squared minus n right parenthesis . Everyone at a party shook hands. There were 171 handshakes in all. How many people attended the? party?

Answer:19Step-by-step explanation:Here we have to find out number of people attended the party. we are given with the number of the handshakes in the party . We are going to use the following formula to determine the number of guests Nos. of handshakes[tex]H=\frac{1}{2}(n^2-n)[/tex]Here we have H = 171Hence our equation becomes [tex]171=\frac{1}{2}(n^2-n)[/tex]now we solve it by splitting the middle term method [tex]171=\frac{1}{2}(n^2-n)\\2*171 =n^2-n\\n^2-n=342\\n^2-n-342=0\\[/tex]Now we have to find the factors of 342 whose difference to 1. The factors are 19 and 18 in this case. hence we slit our middle term like this[tex]n^2-n-342=0\\n^2-19n+18n-342=0\\n(n-19)+18(n-19)=0\\(n-19)(n+18)=0\\[/tex]Hence either (x+18)=0 or (x-19) =0 Thusx=-18 which is not possible as no of people can not be less than 0 x=19 which will our answer