665 Вправа 665Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 195

665. Розв’яжіть рівняння:

1) ${\displaystyle {(x+1)}^2=}$${\displaystyle 64}$;

${\displaystyle x+1=}$${\displaystyle 8}$ або ${\displaystyle x+1=}$${\displaystyle -8}$;

${\displaystyle x=}$${\displaystyle 7}$ або ${\displaystyle x=}$${\displaystyle -9}$;

2) ${\displaystyle {(x-3)}^2=}$${\displaystyle 5}$;

${\displaystyle x-3=}$${\displaystyle \sqrt{5}}$ або ${\displaystyle x-3=}$${\displaystyle -\sqrt{5}}$;

${\displaystyle x=}$${\displaystyle 3+\sqrt{5}}$ або ${\displaystyle x=}$${\displaystyle 3-\sqrt{5}}$;

3) ${\displaystyle {(x-10)}^2=}$${\displaystyle 0}$;

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

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

4) ${\displaystyle {(x+12)}^2-36=}$${\displaystyle 0}$;

${\displaystyle {(x+12)}^2=}$${\displaystyle 36}$;

${\displaystyle x+12=}$${\displaystyle 6}$ або ${\displaystyle x+12=}$${\displaystyle -6}$;

${\displaystyle x=}$${\displaystyle -6}$ або ${\displaystyle x=}$${\displaystyle -18}$;

5) ${\displaystyle {(x+9)}^2-81=}$${\displaystyle 0}$;

${\displaystyle {(x+9)}^2=}$${\displaystyle 81}$;

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

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle -18}$;

6) ${\displaystyle {(x-9)}^2-3=}$${\displaystyle 0}$;

${\displaystyle {(x-9)}^2=}$${\displaystyle 3}$;

${\displaystyle x-9=}$${\displaystyle \sqrt{3}}$ або ${\displaystyle x-9=}$${\displaystyle -\sqrt{3}}$;

${\displaystyle x=}$${\displaystyle 9+\sqrt{3}}$ або ${\displaystyle x=}$${\displaystyle 9-\sqrt{3}}$;

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

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

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

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

8) ${\displaystyle {(x-10)}^2+320=}$${\displaystyle 0}$;

${\displaystyle {(x-10)}^2=}$${\displaystyle -320<0}$;

коренів немає;

9) ${\displaystyle {(x+8)}^2+8=}$${\displaystyle 0}$;

${\displaystyle {(x+8)}^2=}$${\displaystyle -8<0}$;

коренів немає;

10) ${\displaystyle -{(x-10)}^2-10=}$${\displaystyle 0}$;

${\displaystyle {(x-10)}^2=}$${\displaystyle -10<0}$;

коренів немає.