257 Вправа 257Алгебра 8 клас Бевз 2025 · § 5 · стор. 54

257. Задача Р. Декарта (1596–1650). Знайди y: y³ − 8y² − y + 8 = 0.

${\displaystyle y^3-8y^2-y+8=}$${\displaystyle 0}$;

${\displaystyle y^2(y-8)-(y-8)=}$${\displaystyle 0}$;

${\displaystyle (y-8)(y^2-1)=}$${\displaystyle 0}$;

${\displaystyle (y-8)(y-1)(y+1)=}$${\displaystyle 0}$;

${\displaystyle y=}$${\displaystyle 8}$, ${\displaystyle y=}$${\displaystyle 1}$, ${\displaystyle y=}$${\displaystyle -1}$.