Question

Решите систему уравнений:

Answer 1

$\sqrt{x+y}=a\\ \sqrt{x-y}=b \\ \left \{ {{5a-2b=1} \atop {3a-2b=5}} \right. \left \{ {{5a-2b=1} \atop {-3a+2b=5}} \right.\\2a=6\\a=3\\15-2b=1\\-2b=-14\\b=7\\ \left \{ {{ \sqrt{x+y}=3 } \atop { \sqrt{x-y}=7 }} \right. \left \{ {{x+y=9} \atop {x-y=49}} \right. \\2x=58\\x=29\\29+y=9\\y=-20$