Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is
The formula to calculate the total number of handshakes when n people shake hands with each other exactly once is:
Given that the total number of handshakes is 66, we set up the equation:
Step 1: Solve for n
Now, we find nnn by solving the quadratic equation:
Using the quadratic formula:
Taking the positive root:
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