Party

At a party, everyone clinked glasses with everyone else. They clinked 45 times in total. How many people were at the party?

Final Answer:

x =  10

Step-by-step explanation:

(2n​)=45 (2n​) = 2!(n−2)!n!​ = 2n(n−1)​  n(n−1)/2=45  0.5n2−0.5n−45=0  a=0.5;b=−0.5;c=−45 D=b2−4ac=0.52−4⋅0.5⋅(−45)=90.25 D>0  n1,2​=2a−b±D​​=10.5±90.25​​ n1,2​=0.5±9.5 n1​=10 n2​=−9  n>0  x=n1​=10

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