SOLUTION: the product of two consecutive even numbers is 2208.what is the greatest number? (note:i want short cut method)

Question 695852: the product of two consecutive even numbers is 2208.what is the greatest number?
(note:i want short cut method)
Found 2 solutions by mouk, mananth:
Answer by mouk(232) (Show Source): You can put this solution on YOUR website!
Suppose the two consecutive even numbers are 2n and 2n+2

So or

When n=23:
The two consecutive even numbers would be and
ie 46 and 48 (whose product is 2208)

When n=-24:
The two consecutive even numbers would be and
ie -48 and -46 (whose product is 2208)

So to answer the question, greatest number is 48
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x(x+ 2)=2208
x^+2 x +1=2208+1
(x+1)^2 =2209
take the square root
x+1=+/- 47
x= 46
46,48
or
-48,-46
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