673 Вправа 673Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 196

673. Розв’яжіть рівняння:

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

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

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

Якщо ${\displaystyle x=}$${\displaystyle -1}$, то ${\displaystyle \sqrt{x-2}}$ не має змісту (${\displaystyle -1-2<0}$);

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

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

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

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

3) ${\displaystyle x\sqrt{x-10}=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle \sqrt{x-10}=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle 10}$;

Якщо ${\displaystyle x=}$${\displaystyle 0}$, то ${\displaystyle \sqrt{x-10}}$ не має змісту (${\displaystyle 0-10<0}$);

${\displaystyle x=}$${\displaystyle 10}$;

4) ${\displaystyle x\sqrt{x+4}=}$${\displaystyle 0}$;

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

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

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

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

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

${\displaystyle x=}$${\displaystyle -1}$ або ${\displaystyle \sqrt{x}=}$${\displaystyle 1,x=}$${\displaystyle 1}$;

Якщо ${\displaystyle x=}$${\displaystyle -1}$, то ${\displaystyle \sqrt{x}}$ не має змісту;

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

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

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

${\displaystyle x=}$${\displaystyle 1}$ або ${\displaystyle \sqrt{x}=}$${\displaystyle 1,x=}$${\displaystyle 1}$;

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

7) ${\displaystyle x(\sqrt{x}-10)=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle \sqrt{x}-10=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle \sqrt{x}=}$${\displaystyle 10}$;

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle 100}$;

8) ${\displaystyle 2x\sqrt{x}=}$${\displaystyle 0}$;

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

${\displaystyle x=}$${\displaystyle 0}$.