No . of diagonals of polygon

Geometry Level 2

If the number of diagonals of a regular n 2 n^2 -sided polygon is n 3 n^3 , find the value of n n .


The answer is 3.

Tommy Li by Tommy Li , 22, Hong Kong

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1 solution

Tommy Li
Mar 30, 2018

C 2 n 2 − n 2 = n 3 n 2 ( n 2 − 1 ) 2 − n 2 − n 3 = 0 n 2 ( n 2 − 2 n − 3 ) = 0 n 2 ( n + 1 ) ( n − 3 ) = 0 n = − 1 (rej.) or n = 0 (rej.) or n = 3 \large C^{n^2}_{2}-n^2 = n^3 \\ \frac{n^2(n^2-1)}{2} -n^2-n^3 =0 \\ n^2(n^2-2n-3) =0 \\ n^2(n+1)(n-3) =0 \\ n =-1 \text{(rej.) or } n=0 \text{(rej.) or} \ n =3

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