237° Вправа 237Алгебра 8 клас Тарасенкова 2025 · § 7 · стор. 73

237. Розв’яжіть рівняння:

Добуток дорівнює нулю, якщо хоча б один із множників дорівнює нулю.

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

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x-4=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle 4}$;

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

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle 1-3x=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle -3x=}$${\displaystyle -1}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle \frac{1}{3}}$;

3) ${\displaystyle (x+1)(x-4)=}$${\displaystyle 0}$;

${\displaystyle x+1=}$${\displaystyle 0}$ або ${\displaystyle x-4=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle -1}$ або ${\displaystyle x=}$${\displaystyle 4}$;

4) ${\displaystyle (x+2)(5x-1)=}$${\displaystyle 0}$;

${\displaystyle x+2=}$${\displaystyle 0}$ або ${\displaystyle 5x-1=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle -2}$ або ${\displaystyle 5x=}$${\displaystyle 1}$;

${\displaystyle x=}$${\displaystyle -2}$ або ${\displaystyle x=}$${\displaystyle 0,2}$;

5) ${\displaystyle x^2-6x=}$${\displaystyle 0}$;

${\displaystyle x(x-6)=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x-6=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle 6}$;

6) ${\displaystyle x^2+5x=}$${\displaystyle 0}$;

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

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x+5=}$${\displaystyle 0}$;

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

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

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

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

${\displaystyle x=}$${\displaystyle 2}$ або ${\displaystyle x=}$${\displaystyle -2}$;

8) ${\displaystyle 50-2x^2=}$${\displaystyle 0}$;

${\displaystyle 2(25-x^2)=}$${\displaystyle 0}$;

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

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

${\displaystyle x=}$${\displaystyle 5}$ або ${\displaystyle x=}$${\displaystyle -5}$.