11.1. Solve the equation $2 \cos ^{2} x+\sqrt{\cos x}=3$.
Answer: $\quad x=2 \pi k, k \in Z$.

Solution. Since $2 \cos ^{2} x+\sqrt{\cos x} \leq 2 \cdot 1+1=3$, the equality can only hold if $\cos x=1$, from which the answer follows.