Вправи 888 - 1000 » 994 (б)

б) |2x2 – 3x – 1| = 1; 2x2 – 3x – 1 = 1 або 2х2 – 3х – 1 = –1; 1) 2х2 – 3х – 1 = 1; 2x2 – 3x – 1 – 1 = 0; 2x2 – 3x – 2 = 0; D = (–3)2 – 4 • 2 • (–2) = 9 + 16 = 25 = 52; x1 = (3-5)/4 = (-2)/4 = –0,5; x2 = (3+5)/4 = 8/4 = 2; 2) 2x2 – 3x – 1 = –1; 2x2 – 3x – 1 + 1 = 0; 2x2 – 3x = 0; x(2x – 3) = 0; x = 0 або 2x – 3 = 0; 2x = 3 (: 2) ; x = 1,5. Відповідь: –0,5; 0; 1,5; 2.