Question

the product of two consecutive even numbers is 12768 what is the greatest number?

Answer 1

Define x:

Let the smaller number be x.

smaller number = x

greater number = x + 2

.

Product of 2 consecutive number is 12768:

x(x + 2) = 12768

x² + 2x - 12768 = 0

(x - 112) (x + 114) = 0

x = 112 or x = - 144 (rejected, because question asked for greatest)

-

Find the number:

smaller number = x = 112

greater number = x + 2 = 112 + 2 = 114

.

Answer: The greatest number is 114

Answer 2

Heya !!




Let two consecutive even numbers be X and X + 2.






A/Q





X ( X + 2) = 12768



X² + 2X = 12768



X² + 2X - 12768 = 0




x² + 114X - 112X - 12768 = 0




X ( X + 114 ) - 112 ( X + 114 ) = 0



( X + 114 ) ( X - 112 ) = 0




( X + 114 ) = 0 OR ( X - 112 ) = 0




X = 112 OR X = -114.





First number = X = 112.


Second number = X + 2 = 112 + 2 = 114.






Clearly , 114 is greater than 112. So 114 is the greatest number.