Вправи для повторення розділу 3 » 54 (3)

3) x2 – 3x = 8/(x^2- 3x-2). Заміна x2 – 3x = t; t = 8/(t-2); t2 – 2t = 8, t ≠ 2. t2 – 2t – 8 = 0; D = (–2)2 – 4 • (–8) = 36; t1 = (2+6)/2 = 4; t2 = (2-6)/2 = –2. 1) t = 4; x2 – Зх = 4; x2 – Зх – 4 = 0; D = (–3)2 – 4 • (–4) = 25; x1 = (3+5)/2 = 4; x2 = (3-5)/2 = –1. 2) t = –2; x2 – Зх = –2; х2 – Зх + 2 = 0; D = (–3)2 – 4 • 2 = 1; x3 = (3+1)/2 = 2; x4 = (3-1)/2 = 1. Відповідь: –1; 1; 2; 4.