[latex] \left \{ {{ \sqrt{x} - \sqrt{y}=1 } \atop{ \sqrt{x} + \sqrt{y}=19} \right. [/latex]

Решение смотри на фото

[latex] \left \{ {{ \sqrt{x} - \sqrt{y} =1 } \atop { \sqrt{x} + \sqrt{y} = 19}} \right. \\\\\\ \left \{ {{\sqrt{x}-\sqrt{y}=1} \atop {\sqrt{x}+\sqrt{y}=19}} \right.\\\\\ a=\sqrt{b}\; c=\sqrt{y}\; \; \to \; \; \left \{ {{a-b=1} \atop {a+b=19}} \right. \\\\{2b=18}} \right. \\\\ \left { {{a=10} \atop {b=9}}\\ \right. \\\\ \left \{ {{\sqrt{x}=10} \atop {\sqrt{y}=9}} \\ \right. \\\\ \left \{ {{x=100} \atop {y=81}} \right. [/latex]