Вправи 1001 - 1100 » 1001 (б)

б) x/(x-4) – (x-4)/x = –4; x/(x-4) = t, t ≠ 0; 5t – 1/t = –4; 5t\t – 1/t + 4\t = 0; (〖5t〗^2-1+4t)/t = 0 (×t); 5t2 + 4t – 1 = 0; D = 42 – 4 • 5 • (–1) = 16 + 20 = 36 = 62. t1 = (-4-6)/10 = (-10)/10 = –1; t2 = (-4+6)/10 = 2/10 = 1/5; x/(x-4) = –1; x/(x-4) = 1/5. x = –x + 4; 5x = x – 4; x + x = 4; 5x – x = –4; 2x = 4 (: 2); 4x = –4 (: 4); x = 2. x = –1. Відповідь: –1; 2.