919 Вправа 919Алгебра 8 клас Бевз 2025 · § 18 · стор. 175

919. Розв’яжи рівняння.

а) ${\displaystyle 3{(x-5)}^2=}$${\displaystyle 0}$;

${\displaystyle {(x-5)}^2=}$${\displaystyle 0}$;

${\displaystyle x-5=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 5}$;

б) ${\displaystyle {(x-3)}^2=}$${\displaystyle 1}$;

${\displaystyle x-3=}$${\displaystyle 1\text{або }x-3=}$${\displaystyle -1}$;

${\displaystyle x_1=}$${\displaystyle 4,x_2=}$${\displaystyle 2}$;

в) ${\displaystyle 3{(5-y)}^2=}$${\displaystyle 12}$;

${\displaystyle {(5-y)}^2=}$${\displaystyle 4}$;

${\displaystyle 5-y=}$${\displaystyle 2\text{або }5-y=}$${\displaystyle -2}$;

${\displaystyle y_1=}$${\displaystyle 3,y_2=}$${\displaystyle 7}$;

г) ${\displaystyle x^2-6x+9=}$${\displaystyle 0}$;

${\displaystyle {(x-3)}^2=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 3}$;

ґ) ${\displaystyle 3x^2+36x=}$${\displaystyle -108}$;

${\displaystyle 3x^2+36x+108=}$${\displaystyle 0}$;

${\displaystyle x^2+12x+36=}$${\displaystyle 0}$;

${\displaystyle {(x+6)}^2=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle -6}$.