Question

решить систему $\left \{ {{lg (x^2 - y^2) = 2} \atop {log48 x + log48 y =1}} \right.$

Answer 1

{x² - y² = 10²
{x*y=48

{y = 48/x
{x² - 48²/x² = 100

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

Ответ: (√(50 + 2√1201); 48/√(50 + 2√1201)); (-√(50 + 2√1201); -48/√(50 + 2√1201))