РОЗДІЛ 4. Квадратні рівняння » 818 (5-6)

5) (х^2-3х-10)/(х^2-8х+15) = ((х+2)(х-5))/((х-3)(х-5)) = (х+2)/(х-3); x1 + x2 = 3; x1 • x2 = 10; x1 = –2; x2 = 5. х3 + x4 = 8; x3 • x4 = 15; x3 = 3; x4 = 5. 6) (х^2+9х+8)/(-х^2+8х+9) = ((х+1)(х+8))/(-(х-9)(х+1)) = (х+8)/(9-х); x² + 9x + 8 = (x + 1)(x + 8); x1 + x2 = –9; x1 • x2 = 8; x1 = –1; x2 = –8. –x² + 8x + 9 = –(x – 9)(x + 1); D = 82 – 4 • (–1) • 9 = 64 + 36 = 100; х3 = (-8-√100)/(2•(-1)) = (-8-10)/(-2) = (-18)/(-2) = 9; x4 = (-8+√100)/(2•(-1)) = (-8+10)/(-2) = 2/(-2) = –1.