30 Вправа 30 (повторення)Алгебра 8 клас Тарасенкова 2025 · Повторення · стор. 319

30. Розв’яжіть рівняння:

1) ${\displaystyle x^2=}$${\displaystyle 81}$;

${\displaystyle x=}$${\displaystyle \sqrt{81}}$ або ${\displaystyle x=}$${\displaystyle -\sqrt{81}}$;

${\displaystyle x=}$${\displaystyle 9}$ або ${\displaystyle x=}$${\displaystyle -9}$;

2) ${\displaystyle 4x^2=}$${\displaystyle 36}$;

${\displaystyle x^2=}$${\displaystyle 36:4}$;

${\displaystyle x^2=}$${\displaystyle 9}$;

${\displaystyle x=}$${\displaystyle \sqrt{9}}$ або ${\displaystyle x=}$${\displaystyle -\sqrt{9}}$;

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

3) ${\displaystyle x^2-21=}$${\displaystyle 0}$;

${\displaystyle x^2=}$${\displaystyle 21}$;

${\displaystyle x=}$${\displaystyle \sqrt{21}}$ або ${\displaystyle x=}$${\displaystyle -\sqrt{21}}$;

4) ${\displaystyle x^2+17=}$${\displaystyle 0}$;

${\displaystyle x^2=}$${\displaystyle -17}$;

коренів немає, бо ${\displaystyle x^2\ge 0}$;

5) ${\displaystyle {(x-0,5)}^2=}$${\displaystyle 1}$;

${\displaystyle x-0,5=}$${\displaystyle \sqrt{1}}$ або ${\displaystyle x-0,5=}$${\displaystyle -\sqrt{1}}$;

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

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

6) ${\displaystyle {(x-8,1)}^2+81=}$${\displaystyle 0}$;

${\displaystyle {(x-8,1)}^2=}$${\displaystyle -81}$;

коренів немає, бо ${\displaystyle {(x-8,1)}^2\ge 0}$.