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

Question

anonymous · Answer

guess and check for this one

parthkohli · Answer

Why? Why not the great old algebra?

parthkohli · Answer

$\Rightarrow x(x + 2) = 12,320 $
$\Rightarrow x^2 + 2x - 12,320 = 0$

parthkohli · Answer

Seems like you need Wolfram..

anonymous · Answer

ok here is why not the great old algebra

anonymous · Answer

solving $x^2+2x-12320=0$ by factoring is identical to solving the original problem, guess at two numbers that are two apart,whose product is 12320

parthkohli · Answer

I am failing at Mathematics so Idk. 8th grade math is hard D:

anonymous · Answer

lets try 124 and 126
$124\times 126=15,624$ ok that is not it, try a smaller pair

parthkohli · Answer

Wow, my guess worked at the first time. I am not telling what I got as it would be great for fiends.

anonymous · Answer

i guess one hint is that they are both even and it ends in a zero
so a good chance that one of the two numbers ends in a zero as well

anonymous · Answer

$118\times 120=14160$ nope still too big
try $110$

parthkohli · Answer

The superior Satellite ^

ganeshie8 · Answer

one more hint : since the product somewhat large, in @ParthKohli  equation, $x^2$ term dominates.

a good first guess would be around square root of the product

anonymous · Answer

$$2n(2n+2)=12320$$$$4 n^2+4 n-12320=0 $$$$4 (n-55) (n+56)=0 $$n=55$$\{2*55,(2*55+2)\} \text{ -$>$} \{110,112\}, 110*112 = 12320 $$