§ 44: 44.36 (1)

44.36 Розв’яжіть систему рівнянь:

1) 6х – 6y = 1; 6x = a; a – b = 1.

x – y = 7; 6y = b; a³ – b³ = 7.

a = b + 1; b³ + 3b² + 3b + 1 – b³ – 7 = 0;

(b + 1)³ – b³ = 7; 3b² + 3b – 6 = 0;

b² + b – 2 = 0;

b₁ = –2, b₂ = 1.

b = –2; b = –2; 6y = –2;

a = –2 + 1; a = –1; 6x = –1. ∅;

b = 1; b = 1; 6y = 1; y = 1;

a = 1 + 1; a = 2; 6x = 2; x = 64.

Відповідь: (64; 1).

2) 3x-2y2x + 2x3x-2y = 2;

x² – 8y² = 18 – 18y;

3x-2y2x = t; t + 1t = 2; t = 1.

3x-2y2x = 1; 3x – 2y = 2x; x = 2y;

x² – 8y² = 18 – 18y; x² – 8y² = 18 – 18y; (2y)² – 8y² = 18 – 18y;

4y² – 8y² + 18y – 18 = 0;

–4y² + 18y – 18 = 0;

2y² – 9y + 9 = 0; y₁ = 9+34 = 3;

D = 81 – 4 • 2 • 9 = 9;

y₁ = 9+34 = 3; y₂ = 9-34 = 64 = 32; x = 6, x = 3.

Відповідь: (6; 3); (3; 1,5).