Question

The product of two consecutive positive even integers is 12,320. What are the two integers?

Answer 1

Let the even numbers be 2m and 2m+2
2m*(2m+2) = 12320
=> 4n(m+1) = 12320
=> m(m+1) = 3080

now 3080 = 55*56

Thus, m = 55, m+1 = 56
Thus the two even numbers are 2*55 and 2*55 + 2
i.e. 110 and 112

Answer 2

See, first thing to be noted is Even Integer has a difference of 2, i.e, 2, 4, 6 like that..

Let the first even integer be x and the next consecutive even integer will be: x + 2.

So, their product is given as 12,320..

So, x(x + 2) = 12320

\[x^2 + 2x -12320 = 0\]

\[x^2 + 112x - 110x - 12320 = 0\]

\[x(x+112) - 110(x + 112) = 0\]

\[(x-110)(x + 112) = 0\]

So, x = 110 or x = -112..

As, they are positive even integers, so, we neglect x = -112..

x = 110 and (x + 2) = 110 + 2 = 112

So, the two numbers are : 110 and 112...