Two integers

Two integers, a and b, have a product of 36. What is the least possible sum of a and b?

Correct answer:

s₁ =  -37
s₂ =  12

Step-by-step explanation:

$$\begin{gathered} ab=36 \\ {s}_1=(-36)+(-1)=-37 \end{gathered}$$

$$\begin{gathered} ab=36 \\ {a}_1=1,b_1=36,s_1=37 \\ {a}_2=2,b_2=18,s_2=20 \\ {a}_3=3,b_3=12,s_3=15 \\ {a}_4=4,b_4=9,s_4=13 \\ {a}_5=6,b_5=6,s_5=12 \\ {a}_6=9,b_6=4,s_6=13 \\ {a}_7=12,b_7=3,s_7=15 \\ {a}_8=18,b_8=2,s_8=20 \\ {a}_9=36,b_9=1,s_9=37 \\ a=\sqrt{36}=6 \\ b=36\mathrm{/}a=36\mathrm{/}6=6 \\ {s}_2=a+b=6+6=12 \end{gathered}$$

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