12.5.10 Olympic algebra

Condition: Let the sequence \( \left\{c_{n}\right\} \) have the following relation: \[ c_{n+1}=\sqrt{c_{n}}+\sqrt{c_{n-1}}, n \geq 1, c_{0}>0, c_{1}>0 \] Prove that \( c_{n} \) converges and find its limit.