решить систему [tex] \left \{ {{lg (x^2 - y^2) = 2} \atop {log48 x + log48 y =1}} ight. [/tex]

{x² - y² = 10²{x*y=48{y = 48/x{x² - 48²/x² = 100{y = 48/x{x⁴ - 100x² - 48² = 0D = 10000 + 9216 = 19216 = (4√1201)²x² = (100 + 4√1201)/2 = 50 + 2√1201x = +-√(50 + 2√1201)y = +-48/√(50+2√1201)Ответ: (√(50 + 2√1201); 48/√(50 + 2√1201)); (-√(50 + 2√1201); -48/√(50 + 2√1201))