РОЗДІЛ 4. Квадратні рівняння » 855 (2)

2) (х-2)/(х+2) + (х+2)/(х-2) = 5/2; ОДЗ: х ≠ ±2; t = (х-2)/(х+2) (t ≠ 0); t + 1/t = 5/2; t\2t + 1^(\2)/t – 5^(\t)/2 = 0; (〖2t〗^2+ 2-5t)/2t = 0; 2t2 – 5t + 2 = 0; D = (–5)2 – 4 • 2 • 2 = 25 – 16 = 9; t1 = (5-√9)/(2• 2) = (5-3)/4 = 2/4 = 1/2; t2 = (5+√9)/(2• 2) = (5+3)/4 = 8/4 = 2. (x-2)/(x+2) = 1/2 або 2x – 4 = x + 2; 2x – x = 2 + 4; x = 6. (x-2)/(x+2) = 2; x – 2 = 2x + 4; x – 2x 4 + 2; –x = 6; x = –6. Відповідь: ±6.