б) {lg (x²+y²) = 2, log₄₈ x + log₄₈ y = 1;

б) Решим систему уравнений:

{lg (x^2+y^2) = 2,

{log_{48} x + log_{48} y = 1;

x>0, y>0

{x^2+y^2 = 10^2,

{log_{48} xy = 1;

{x^2+y^2 = 100,

{xy = 48;

x^2+y^2 = 100,

y = \frac{48}{x}

x^2+(\frac{48}{x})^2 = 100,

x^2+\frac{2304}{x^2} = 100,

x^4+2304 = 100x^2,

x^4-100x^2+2304 = 0,

z = x^2,

z^2-100z+2304 = 0,

D = 10000-4\cdot2304=10000-9216=784,

\sqrt{D} = 28,

z_1 = \frac{100+28}{2}=\frac{128}{2}=64,

z_2 = \frac{100-28}{2}=\frac{72}{2}=36,

x^2=64,

x_1=8, x_2=-8 -не подходит

x^2=36,

x_3=6, x_4=-6 -не подходит

Найдем у:

y_1 = \frac{48}{8}=6

y_2 = \frac{48}{6}=8

Проверка:

{lg (8^2+6^2) = 2,

{log_{48} 8 + log_{48} 6 = 1;

{lg (64+36) = 2,

{log_{48} 48 = 1;

{lg (100) = 2,

1=1

2=2

Ответ: x_1=8, y_1 = 6; x_2=6, y_2 = 8