Question

a² = 2013 + b²
Find the minimum value of a*b. (Steps Please)

Answer 1

a^2=2013-b^2
=> a^2 - b^2=2013
=>(a+b)(a-b)=2013
Now prime factors of 2013 are
1 ×2013
3×671
11×183
33×61
many values of a & b are possible

Take (a+b) as one of the factors & (a-b) as the other so that (a+b)(a-b)=2013
then find the solution.

For eg. if you take (a+b)=61 ––––-(1)
then (a-b)=33-–––--(2)
Adding equation (1) & (2)
we get
a+b+a-b=33+61
2a=94
a=94/2=47
so b=61-a ( from equation (1) )
b=61-47=14

HOPE IT HELPS....