РОЗДІЛ 4. Квадратні рівняння » 854 (4)

4) (x+3)/(х-3) + (x-3)/(х+3) = 10/3; ОДЗ: х ≠ ±3; t = (x+3)/(x-3), (t ≠ 0); t + 1/t = 10/3; t^(\3t)/(х+3) + 1/t – 10^(\t)/3 = 0; ( 〖3t〗^2+ 3-10t)/t = 0; 3t2 – 10t + 3 = 0; D = (–10)2 – 4 • 3 • 3 = 100 – 36 = 64; t1 = (10-√64)/(2• 3) = (10-8)/6 = 2/6 = 1/3; t2 = (10+√64)/(2• 3) = (10+8)/69 = 18/6 = 3. (x+3)/(x-3) = 1/3 або 3x + 9 = x – 3; 3x – x = –3 – 9; 2x = –12; x = –6. (x+3)/(x-3) = 3; x + 3 = 3x – 9; x – 3x = –9 – 3; –2x = –12; x = 6. Відповідь: –6; 6.