Question

At a party everyone shook hands with everybody else.There were 66 handshakes.Then how many people attended that party.

Answer 1

Let the number of people attended party be n, then ;
Total number of handshakes = n(n-1)/2
66 = n(n-1)/2
n^2-n = 132
n^2-n-132 = 0
n^2+11n-12n-132 = 0
n(n+11) -12(n-12) = 0
(n-12) (n+11) = 0

n = 12 & -11
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but the number of peoples can't be negative, hence there 12 people attended the party.

Answer 2

The formula for handshakes = n(n -1)/2
Where n = number of people

66 = n(n-1)/2
66 x 2 = n^2 - n
n^2 - n - 132 = 0
n^2 + 11n - 12n - 132 = 0
n( n +11) - 12( n + 11) = 0
(n -12)(n+11) =0

n =12 or n = -11

But the number of people can't be negative.

So number of people = 12