(3+
sqrt(10))^(19)
Тогда
{T_(k) > T_(k-1)
{T_(k) > T_(k+1)
T_(k-1)=C^(k-1)_(19)*(3)^(k-1)*(sqrt(10))^(19-k+1)=
=(19!/(k-1)!*(19-k+1)!)3^(k-1)*(sqrt(10))^(19-k+1)
T_(k)=C^(k)_(19)*(3)^(k)*(sqrt(10))^(19-k)=
=(19!/(k)!*(19-k)!)3^(k)*(sqrt(10))^(19-k)
T_(k+1)=C^(k+1)_(19)*(3)^(k+1)*(sqrt(10))^(19-k-1)=
=(19!/(k+1)!*(19-k-1)!)3^(k+1)*(sqrt(10))^(19-k-1)
{(3/k) > sqrt(10)/(19-k+1) ⇒ k < 57/(sqrt(10)+3) ≈ считаем самостоятельно
{sqrt(10)/(19-k) > 3/(k+1) ⇒ k > (57-sqrt(10))/(sqrt(10)+3) ≈ считаем самостоятельно
Тогда легко найти k