Brazil | A nice Math Olympiad Problem | Lambert W Function Algebra |

[@Lemda_gtr]

So smart 🎉

[@BruceLee-io9by]

A very elegant and clean mathematical work. Congratulations!

[@superacademy247]

Many thanks. Glad you like it!

[@BartBuzz]

For this equation, it is not difficult to "see" that Sqrt(a) = 3 is a solution. Applying Lambert W, confirms that 3 is the only solution.

[@superacademy247]

Thanks ✅✅✅🙏🙏🙏

[@walterwen2975]

A nice Math Olympiad Problem: 3^√a + √a = 30; a =?
30 > √a > 0, √a ϵN; 3^√a + √a = 30 = 27 + 3 = 3^3 + 3 = 3^√9 + √9; a = 9
Find more answer, if available, using Trial-and-error math:
3 > √a > 0; √a = 1, 2: 3^√a + √a < 30
√a > 3; √a = 4, 5, … : 3^√a + √a > 30, No more answer
Answer check:
a = 9: 3^√a + √a = 30; Confirmed as shown
Final answer:
a = 9

[@cescllopis]

√a = 3 !

[@superacademy247]

Voila!

[@isilsuarslan]

easy

[@superacademy247]

Lambert W Function

[@CTJ2619]

i arrived at x=3 without the use of Lambert W function.

[@superacademy247]

a=9