1.

1 added to the product of two consecutive even numbers gives 289. What are the numbers?

Answer»

Let the two consecutive even numbers be x,

x + 2

x, x + 2 

x(x + 2) + 1 = 289 

x2 + 2x = 288 

x2 + 2x – 288 = 0 

x2 + 2x = 288 

(x+1)2 = 288 + 1 

(x+1)2 = 289 

x + 1 = ± 17 

x = 16, – 18 

The numbers are 16, 18



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