Diagonals

What x-gon has 54 diagonals?

Correct answer:

x =  12

Step-by-step explanation:

54=n(n−3)/2  −0.5n2+1.5n+54=0 0.5n2−1.5n−54=0  a=0.5;b=−1.5;c=−54 D=b2−4ac=1.52−4⋅0.5⋅(−54)=110.25 D>0  n1,2​=2a−b±D​​=11.5±110.25​​ n1,2​=1.5±10.5 n1​=12 n2​=−9  x>0  x=n1​=12

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combinatoricsalgebraplanimetricsUnits of physical quantitiesGrade of the word problem

 
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