1. For what non-zero values of x, is the expression 1+x+x{+2}a perfect square?

2. Find the number of diagonals of a Octagon?

Solution

1) For no values of x.

Explanation: 1+x+x^2 lies between two square numbers x^2 and (x+1)^2.

2) 20.

Explanation: The number of diagonals is (8x5)/2 = 20.