Each of a, b, and c is a real number such that a+b+c=2.
Suppose the minimum value of:
(a+1/a)2 + (b+1/b)2 + (c+1/c)2 is m/n, where gcd(m,n) =1.
Find m+n.
*** Adapted from a problem which appeared at Round 1 of Singapore Mathematical Olympiad Open, 2018.
I did a little searching around. The original problem from the SMO requires a,b,c all be positive.
https://www.intereseducation.com/resources/smo-past-papers-2018-with-solutions-singapore-mathematical-olympiad/
The solution is then when a=b=c=2/3
the expression m/n = 169/12 and m+n=181
Video of solution with proof.
https://www.youtube.com/watch?v=B7QpRfObAX0
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Posted by Jer
on 2025-02-22 13:22:02 |
error in the problem
