Вправи: 1434

1434. Розв’яжи рівняння:

a) 1 + 12+ 13+ 1x = 139; 3 + 1x = 3x+1x; 2 + x3x+1 = 23x+1+ x3x+1 = 7x+23x+1;

1 + 17x+23x+1 = 1 + 3x+17x+2 = 7x+2+3x+17x+2 = 10x+37x+2; 10x+37x+2 = 139;

90x + 27 = –91 + 26; 27 – 26 = 91x – 90x; x = 1.

Відповідь: 1,

б) 1 + 1x+ 11+ 1x = 2924; 1 + 1x = x+1x;

x + 1x+1x = x + xx+1 = x2+ x+xx+1 = x2+ 2xx+1;

1 + 1x2+ 2xx+1 = 1 + x+1x2+ 2x = x2+ 2x+x+1x2+ 2x = x2+ 3x+1x2+ 2x; x2+ 3x+1x2+ 2x = 2924;

24x² + 72x + 24 = 29x² + 58x; 5x² – 14x – 24 = 0;

x = 7 ± 49+1205 = 7 ±135; x₁ = 4; x₂ = –65.

Відповідь: 4; –115.