Two integers

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

Correct result:

s1 =  -37
s2 =  12

Solution:

ab=36 s1=(36)+(1)=37ab=36 \ \\ s_{1}=(-36) + (-1)=-37
ab=36  a1=1,b1=36,s1=37 a2=2,b2=18,s2=20 a3=3,b3=12,s3=15 a4=4,b4=9,s4=13 a5=6,b5=6,s5=12 a6=9,b6=4,s6=13 a7=12,b7=3,s7=15 a8=18,b8=2,s8=20 a9=36,b9=1,s9=37  a=36=6 b=36/a=36/6=6 s2=a+b=6+6=12ab=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/a=36/6=6 \ \\ s_{2}=a + b=6 + 6=12



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