Question

. Tenglamalar sistemasini yeching (Решите систему уравнений): {lg(x²+y²)- 1 =lg 13
{lg(x+y)- lg (x - y)=3lg 2

Answer 1

lg(x²+y²) - 1 = lg13,

lg(x+y) - lg(x - y)=3lg 2;

lg(x²+y²) = lg13 + 1,

lg(x+y) = lg2³ + lg (x - y);

lg(x²+y²) = lg13 + lg10,

lg(x+y) = lg8 + lg (x - y);

lg(x²+y²) = lg130,

lg(x+y) = lg8(x - y);

x² + y² = 130,

x + y = 8(x - y);

x² + y² = 130,

x + y = 8x - 8y;

x² + y² = 130,

9y = 7x;

x² + y² = 130,

y = 7x/9;

x² + 49x²/81 = 130|·81;

81x² + 49x² = 130·81;

130x² = 130·81;

x² = 81;

x₁ = 9; x₂ = -9

y₁ = 7·9/9 = 7; y₂ = -7·9/9 = -7

(-9; -7) - Не задовольняє систему.

Відповідь: (9; 7).