Question 1014219
The product of two consecutive even  
natural numbers is 120.
Find the numbers.
<pre>
In problems like this, sometimes you can just guess them.  
But if you can't, then do it this way:

x = first even integer
x+2 = second even integer

x(x+2) = 120

x² + 2x = 120

x² + 2x - 120 = 0

{{{x = (-b +- sqrt( b^2-4ac ))/(2a) }}}

a=1, b=2, c=-120

{{{x = (-(2) +- sqrt( (2)^2-4(1)(-120) ))/(2(1)) }}}

{{{x = (-2 +- sqrt(4+480 ))/(2(1)) }}}

{{{x = (-2 +- sqrt(484) )/2 }}}

{{{x = (-2 +- 22 )/2 }}}

Using the +

{{{x = (-2 + 22 )/2 }}}

{{{x = 20/2 }}}

{{{x = 10 }}}

So one solution is

x = 10 = first even integer
x+2 = 10+2 = 12 = second even integer

Using the -

{{{x = (-2 - 22 )/2 }}}

{{{x = (-24)/2 }}}

{{{x = -12 }}}

So another solution is

x = -12 = first even integer
x+2 = -12+2 = -10 = second even integer

Edwin</pre>