This is the second step in solving a problem Reygan Dionisio posted on LinkedIn
Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b,
k}]
During evaluation := Solve::nsmet: This system cannot be solved with the methods available to Solve.
Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b,
k}]
MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b,
k}] // FullSimplify
1 + Sqrt[2]
MaxValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b,
k}] // FullSimplify
1 + Sqrt[2]