let's say the first number is -a, so "a" will be some positive value, and we multiply -1 to it, we get the -a
a consecutive number from it, is either, ahead or before it, so, -a + 1 or -a -1, is a consecutive integer, hmm let's use -a + 1 then
so, the two numbers are -a and -a + 1
we know their product is 600
[tex]\bf (-a)(-a+1)=600\implies a^2-a=600
\\\\\\
\begin{array}{lcclll}
a^2&-a&-600=0\\
&\uparrow &\uparrow \\
&-25+24&-25\cdot 24
\end{array} \implies (a-25)(a+24)=0
\\\\\\
\begin{cases}
a-25=0\implies &\boxed{a=25}\\
a+24=0\implies &a=-24
\end{cases}[/tex]
we use the positive one, because we're using -1 in front of the "a"
what's the lesser integer? well, what's -a+1? which one is lesser?
