<s>[INST] Product of numbers Pair of numbers whose product is $+7$ and whose sum is $-8$. 
Factorise $x^{2} - 8x + 7$.
I can factorise but it's just I can't find any products of $+7$ and that is a sum of 
$-8$. Any idea? Thanks guys!
Thanks.
 [/INST] $(x-a)(x-b)=x^2-(a+b)x+ab$
So, you are looking for the roots of $x^2-(+2)x+(-3)$, that is, $x^2-2x-3$, which is $=x^2-2x+1-4=(x-1)^2-4$, and this is $0$ iff $(x-1)^2=4$, that is, $x-1=\pm 2$, i.e., $-1,3$ is your solution.
Similarly for the other one: $x^2-8x+7=(x-4)^2-16+7=\dots$
Or, the other way: $7+1=8$ and $7\cdot 1=7$, so the roots of $x^2-8x+7$ are $1$ and $7$.
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