РОЗДІЛ 4. Квадратні рівняння » 819 (1-2)

819. Скоротіть дріб: 1) (4х+4)/(х^2-5х-6) = (4(х+1))/((х+1)(х-6)) = 4/(х-6); x² – 5x – 6 = (x + 1)(x – 6); x1 + x2 = 5; x1 • x2 = –6; x1 = –1; x2 = 6. 2) (х^2-3х)/(〖3х〗^2-10х+3) = (х(х-3))/((3х-1)(х-3)) = х/(3х-1); 3x² – 10x + 3 = 3(x – 1/3)(x – 3) = (3x – 1)(x – 3); D = (–10)2 – 4 • 3 • 3 = 100 – 36 = 64; x1 = (10-√64)/(2•3) = (10-8)/6 = 2/6 = 1/3; x2 = (10+√64)/(2•3) = (10+8)/6 = 18/6 = 3.