904 Вправа 904Алгебра 8 клас Бевз 2025 · § 18 · стор. 173

904. Розв’яжи рівняння.

а) ${\displaystyle (x-1)x+3x=}$${\displaystyle 0}$;

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

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

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

${\displaystyle x_1=}$${\displaystyle 0,x_2=}$${\displaystyle -2}$;

б) ${\displaystyle 2y(y+5)=}$${\displaystyle 6y}$;

${\displaystyle 2y^2+10y-6y=}$${\displaystyle 0}$;

${\displaystyle 2y^2+4y=}$${\displaystyle 0}$;

${\displaystyle 2y(y+2)=}$${\displaystyle 0}$;

${\displaystyle y_1=}$${\displaystyle 0,y_2=}$${\displaystyle -2}$;

в) ${\displaystyle (z+2)(z-2)=}$${\displaystyle 0}$;

${\displaystyle z^2-4=}$${\displaystyle 0}$;

${\displaystyle z^2=}$${\displaystyle 4}$;

${\displaystyle z=}$${\displaystyle \pm 2}$;

г) ${\displaystyle (x+2)(x-2)=}$${\displaystyle 4}$;

${\displaystyle x^2-4=}$${\displaystyle 4}$;

${\displaystyle x^2=}$${\displaystyle 8}$;

${\displaystyle x=}$${\displaystyle \pm \sqrt{8}}$;

${\displaystyle x=}$${\displaystyle \pm 2\sqrt{2}}$;

ґ) ${\displaystyle 5x^2+3x+7=}$${\displaystyle 7(x+1)}$;

${\displaystyle 5x^2+3x+7=}$${\displaystyle 7x+7}$;

${\displaystyle 5x^2-4x=}$${\displaystyle 0}$;

${\displaystyle x(5x-4)=}$${\displaystyle 0}$;

${\displaystyle x_1=}$${\displaystyle 0,x_2=}$${\displaystyle 0,8}$;

д) ${\displaystyle 2(x^2-1)=}$${\displaystyle (x-1)(x+1)}$;

${\displaystyle 2x^2-2=}$${\displaystyle x^2-1}$;

${\displaystyle x^2=}$${\displaystyle 1}$;

${\displaystyle x=}$${\displaystyle \pm 1}$.