900 Вправа 900Алгебра 8 клас Бевз 2025 · § 18 · стор. 173

900. Розв’яжи рівняння.

а) ${\displaystyle 3x^2-27=}$${\displaystyle 0}$;

${\displaystyle 3x^2=}$${\displaystyle 27}$;

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

${\displaystyle x=}$${\displaystyle \pm 3}$;

б) ${\displaystyle 3x^2+27=}$${\displaystyle 0}$;

${\displaystyle 3x^2=}$${\displaystyle -27}$;

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

коренів немає;

в) ${\displaystyle 0,5y^2+y=}$${\displaystyle 0}$;

${\displaystyle y(0,5y+1)=}$${\displaystyle 0}$;

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

${\displaystyle y_1=}$${\displaystyle 0,y_2=}$${\displaystyle -2}$;

г) ${\displaystyle z-2z^2=}$${\displaystyle 0}$;

${\displaystyle z(1-2z)=}$${\displaystyle 0}$;

${\displaystyle z=}$${\displaystyle 0\text{або }2z=}$${\displaystyle 1}$;

${\displaystyle z_1=}$${\displaystyle 0,z_2=}$${\displaystyle 0,5}$;

ґ) ${\displaystyle x^2-144=}$${\displaystyle 0}$;

${\displaystyle x^2=}$${\displaystyle 144}$;

${\displaystyle x=}$${\displaystyle \pm 12}$;

д) ${\displaystyle 0,16x^2+100=}$${\displaystyle 0}$;

${\displaystyle 0,16x^2=}$${\displaystyle -100}$;

коренів немає;

е) ${\displaystyle 16x^2=}$${\displaystyle 25}$;

${\displaystyle x^2=}$${\displaystyle \frac{25}{16}}$;

${\displaystyle x=}$${\displaystyle \pm \frac{5}{4}}$;

${\displaystyle x=}$${\displaystyle \pm 1,25}$;

є) ${\displaystyle -4y^2=}$${\displaystyle 0}$;

${\displaystyle y^2=}$${\displaystyle 0}$;

${\displaystyle y=}$${\displaystyle 0}$;

ж) ${\displaystyle (\sqrt{7}-\sqrt{3})x^2=}$${\displaystyle 0}$;

коефіцієнт ${\displaystyle \sqrt{7}-\sqrt{3}\ne 0}$, тому ${\displaystyle x^2=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$.