Fractions With Twists And Turns
Algebra
Level
4
\[\large \displaystyle \sum_{\text {cyc}} \dfrac{a}{bc+1}\] Let \(a,b\) and \(c\) be positive reals satisfying \(a+b+c=3\).
Find the minimum value of the expression above.
Bonus: Find as many approaches as possible
This problem was taken from Hanoi grade 10 selection test for specialized students
by
Gurīdo Cuong