645° Вправа 645Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 192

645. Розв’яжіть рівняння:

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

2) ${\displaystyle x^2=}$${\displaystyle 36}$; ${\displaystyle x=}$${\displaystyle -6}$; ${\displaystyle x=}$${\displaystyle 6}$;

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

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

5) ${\displaystyle x^2=}$${\displaystyle 11}$; ${\displaystyle x=}$${\displaystyle \pm \sqrt{11}}$;

6) ${\displaystyle x^2=}$${\displaystyle 15}$; ${\displaystyle x=}$${\displaystyle \pm \sqrt{15}}$;

7) ${\displaystyle x^2-64=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle 64}$; ${\displaystyle x=}$${\displaystyle \pm 8}$;

8) ${\displaystyle 2x^2-42=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle 21}$; ${\displaystyle x=}$${\displaystyle \pm \sqrt{21}}$;

9) ${\displaystyle x^2-81=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle 81}$; ${\displaystyle x=}$${\displaystyle \pm 9}$;

10) ${\displaystyle x^2-17=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle 17}$; ${\displaystyle x=}$${\displaystyle \pm \sqrt{17}}$;

11) ${\displaystyle x^2=}$${\displaystyle -1<0}$; коренів немає;

12) ${\displaystyle x^2=}$${\displaystyle -29<0}$; коренів немає;

13) ${\displaystyle x^2=}$${\displaystyle -62<0}$; коренів немає;

14) ${\displaystyle x^2=}$${\displaystyle -100<0}$; коренів немає;

15) ${\displaystyle x^2+13=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle -13<0}$; коренів немає;

16) ${\displaystyle x^2+40=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle -40<0}$; коренів немає;

17) ${\displaystyle 0,1x^2+1,6=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle -16<0}$; коренів немає;

18) ${\displaystyle \frac{x^2}{4}-16=}$${\displaystyle 0}$; ${\displaystyle x^2=}$${\displaystyle 64}$; ${\displaystyle x=}$${\displaystyle \pm 8}$.