Решите систему уравнений
Так как при всех допустимых , получаем, что Значит, при решений нет.
Ответ: (25; 64).
![a=\sqrt{x};b=\sqrt[3]{y}.\\\left \{ {{a-b=1,} \atop {ab=20;}} \right.\\\left \{ {{b=a-1,} \atop {a(a-1)=20.}} \right.\\ a(a-1)=20;\\a^2-a-20=0;\\\left \{ {{a_1+a_2=1,} \atop {a_1a_2=-20;}} \right. \\a_1=-4,\\a_2=5.\\](https://tex.z-dn.net/?f=a%3D%5Csqrt%7Bx%7D%3Bb%3D%5Csqrt%5B3%5D%7By%7D.%5C%5C%5Cleft%20%5C%7B%20%7B%7Ba-b%3D1%2C%7D%20%5Catop%20%7Bab%3D20%3B%7D%7D%20%5Cright.%5C%5C%5Cleft%20%5C%7B%20%7B%7Bb%3Da-1%2C%7D%20%5Catop%20%7Ba%28a-1%29%3D20.%7D%7D%20%5Cright.%5C%5C%20a%28a-1%29%3D20%3B%5C%5Ca%5E2-a-20%3D0%3B%5C%5C%5Cleft%20%5C%7B%20%7B%7Ba_1%2Ba_2%3D1%2C%7D%20%5Catop%20%7Ba_1a_2%3D-20%3B%7D%7D%20%5Cright.%20%5C%5Ca_1%3D-4%2C%5C%5Ca_2%3D5.%5C%5C "a=\sqrt{x};b=\sqrt[3]{y}.\\\left \{ {{a-b=1,} \atop {ab=20;}} \right.\\\left \{ {{b=a-1,} \atop {a(a-1)=20.}} \right.\\ a(a-1)=20;\\a^2-a-20=0;\\\left \{ {{a_1+a_2=1,} \atop {a_1a_2=-20;}} \right. \\a_1=-4,\\a_2=5.\\")
при всех допустимых 
, получаем, что 
Значит, при 
решений нет.![\left \{ {{a=5,} \atop {b=5-1;}} \right. \\\left \{ {{a=5,} \atop {b=4.}} \right.\\\left \{ {{\sqrt{x} =5,} \atop {\sqrt[3]{y} =4;}} \right.\\\left \{ {{x=25,} \atop {y=64.}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Ba%3D5%2C%7D%20%5Catop%20%7Bb%3D5-1%3B%7D%7D%20%5Cright.%20%5C%5C%5Cleft%20%5C%7B%20%7B%7Ba%3D5%2C%7D%20%5Catop%20%7Bb%3D4.%7D%7D%20%5Cright.%5C%5C%5Cleft%20%5C%7B%20%7B%7B%5Csqrt%7Bx%7D%20%3D5%2C%7D%20%5Catop%20%7B%5Csqrt%5B3%5D%7By%7D%20%3D4%3B%7D%7D%20%5Cright.%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx%3D25%2C%7D%20%5Catop%20%7By%3D64.%7D%7D%20%5Cright. "\left \{ {{a=5,} \atop {b=5-1;}} \right. \\\left \{ {{a=5,} \atop {b=4.}} \right.\\\left \{ {{\sqrt{x} =5,} \atop {\sqrt[3]{y} =4;}} \right.\\\left \{ {{x=25,} \atop {y=64.}} \right.")