730° Вправа 730Алгебра 8 клас Тарасенкова 2025 · § 17 · стор. 216

730. Розв’яжіть рівняння:

1) ${\displaystyle {(x+7)}^2=}$${\displaystyle 49}$;

${\displaystyle x+7=}$${\displaystyle \sqrt{49}}$ або ${\displaystyle x+7=}$${\displaystyle -\sqrt{49}}$;

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

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

${\displaystyle x=}$${\displaystyle 0}$ або ${\displaystyle x=}$${\displaystyle -14}$;

2) ${\displaystyle {(x-3)}^2=}$${\displaystyle 16}$;

${\displaystyle x-3=}$${\displaystyle \sqrt{16}}$ або ${\displaystyle x-3=}$${\displaystyle -\sqrt{16}}$;

${\displaystyle x-3=}$${\displaystyle 4}$ або ${\displaystyle x-3=}$${\displaystyle -4}$;

${\displaystyle x=}$${\displaystyle 4+3}$ або ${\displaystyle x=}$${\displaystyle -4+3}$;

${\displaystyle x=}$${\displaystyle 7}$ або ${\displaystyle x=}$${\displaystyle -1}$;

3) ${\displaystyle {(x-5)}^2=}$${\displaystyle 36}$;

${\displaystyle x-5=}$${\displaystyle \sqrt{36}}$ або ${\displaystyle x-5=}$${\displaystyle -\sqrt{36}}$;

${\displaystyle x-5=}$${\displaystyle 6}$ або ${\displaystyle x-5=}$${\displaystyle -6}$;

${\displaystyle x=}$${\displaystyle 6+5}$ або ${\displaystyle x=}$${\displaystyle -6+5}$;

${\displaystyle x=}$${\displaystyle 11}$ або ${\displaystyle x=}$${\displaystyle -1}$;

4) ${\displaystyle {(x+4)}^2=}$${\displaystyle 1}$;

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

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

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

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

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

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

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

6) ${\displaystyle {(x-1)}^2=}$${\displaystyle -25}$;

${\displaystyle {(x-1)}^2\ge 0}$, а ${\displaystyle -25<0}$;

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