253 Вправа 253Алгебра 8 клас Тарасенкова 2025 · § 7 · стор. 76

253. Розв’яжіть рівняння:

1) ${\displaystyle \frac{x+1}{x^3+1}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle x^3+1\ne 0}$;

${\displaystyle (x+1)(x^2-x+1)\ne 0}$;

${\displaystyle x\ne -1}$;

${\displaystyle x+1=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle -1}$ — не задовольняє ОДЗ;

коренів немає;

2) ${\displaystyle \frac{x-4}{64-x^3}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 64-x^3\ne 0}$;

${\displaystyle (4-x)(16+4x+x^2)\ne 0}$;

${\displaystyle x\ne 4}$;

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

${\displaystyle x=}$${\displaystyle 4}$ — не задовольняє ОДЗ;

коренів немає;

3) ${\displaystyle \frac{3x^2-3}{4x+4}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 4x+4\ne 0}$;

${\displaystyle 4(x+1)\ne 0}$;

${\displaystyle x\ne -1}$;

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

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

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

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

${\displaystyle x=}$${\displaystyle -1}$ — не задовольняє ОДЗ;

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

4) ${\displaystyle \frac{2x^2-18}{9-3x}=}$${\displaystyle 0}$;

ОДЗ: ${\displaystyle 9-3x\ne 0}$;

${\displaystyle 3(3-x)\ne 0}$;

${\displaystyle x\ne 3}$;

${\displaystyle 2(x^2-9)=}$${\displaystyle 0}$;

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

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

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

${\displaystyle x=}$${\displaystyle 3}$ — не задовольняє ОДЗ;

${\displaystyle x=}$${\displaystyle -3}$.