907 Вправа 907Алгебра 8 клас Бевз 2025 · § 18 · стор. 174

907. Розв’яжи рівняння: а) (x² − 1)/7 = 3/4; б) (2x² + 3)/5 = 4/7; в) (y − 2)/4 = −1/(y + 2).

а) ${\displaystyle \frac{x^2-1}{7}=}$${\displaystyle \frac{3}{4}}$;

${\displaystyle 4(x^2-1)=}$${\displaystyle 21}$;

${\displaystyle 4x^2=}$${\displaystyle 25}$;

${\displaystyle x^2=}$${\displaystyle \frac{25}{4}}$;

${\displaystyle x=}$${\displaystyle \pm 2,5}$;

б) ${\displaystyle \frac{2x^2+3}{5}=}$${\displaystyle \frac{4}{7}}$;

${\displaystyle 7(2x^2+3)=}$${\displaystyle 20}$;

${\displaystyle 14x^2=}$${\displaystyle -1}$;

коренів немає;

в) ${\displaystyle \frac{y-2}{4}=}$${\displaystyle \frac{-1}{y+2},y\ne -2}$;

${\displaystyle (y-2)(y+2)=}$${\displaystyle -4}$;

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

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

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