1.

9 added to the product of two consecutive multiples of 6 gives 729. What are the numbers?

Answer»

Let the two consecutive multiples of 6 be x,

x + 6

x, x + 6

x(x + 6) + 9 = 729

x2 + 6x + 9 = 729

x2 + 6x = 720 

x2 + 6x – 720 = O 

x + 6x = 720 

(x + 3)2 = 720 + 9 

(x + 3)2 = 729 

x + 3 = ± 27 

x = 24, – 30 

The numbers are 24, – 30



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