1201 Вправа 1201Алгебра 8 клас Бевз 2025 · § 23 · стор. 228

1201. Розв’яжи ребуси, зображені на малюнках 23.5, 23.6.

Мал. 23.5. Позначимо порожні кружечки: на перетині лівої і горизонтальної планок — ${\displaystyle a}$, зверху — ${\displaystyle b}$, справа — ${\displaystyle c}$.

Записи: ${\displaystyle 3\cdot a=}$${\displaystyle b}$;

${\displaystyle 12:a=}$${\displaystyle c}$;

${\displaystyle b+c=}$${\displaystyle 20}$;

${\displaystyle 3a+\frac{12}{a}=}$${\displaystyle 20\mid \cdot a}$;

${\displaystyle 3a^2-20a+12=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 3,b=}$${\displaystyle -20,c=}$${\displaystyle 12}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-20)}^2-4\cdot 3\cdot 12=}$${\displaystyle 400-144=}$${\displaystyle 256}$;

${\displaystyle D>0}$, два корені:

${\displaystyle a_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{20\pm \sqrt{256}}{6}=}$${\displaystyle \frac{20\pm 16}{6}}$;

${\displaystyle a_1=}$${\displaystyle \frac{20+16}{6}=}$${\displaystyle 6}$;

${\displaystyle a_2=}$${\displaystyle \frac{20-16}{6}=}$${\displaystyle \frac{2}{3}}$;

${\displaystyle a=}$${\displaystyle 6}$: ${\displaystyle 3\cdot 6=}$${\displaystyle 18}$;

${\displaystyle 12:6=}$${\displaystyle 2}$;

${\displaystyle 18+2=}$${\displaystyle 20}$;

(при ${\displaystyle a=}$${\displaystyle \frac{2}{3}}$: ${\displaystyle b=}$${\displaystyle 2}$;

${\displaystyle c=}$${\displaystyle 18}$ — теж підходить);

Мал. 23.6. Записи: ${\displaystyle 2+a=}$${\displaystyle b}$;

${\displaystyle 30:a=}$${\displaystyle c}$;

${\displaystyle b-c=}$${\displaystyle 3}$;

${\displaystyle 2+a-\frac{30}{a}=}$${\displaystyle 3\mid \cdot a}$;

${\displaystyle a^2+2a-30=}$${\displaystyle 3a}$;

${\displaystyle a^2-a-30=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 1,b=}$${\displaystyle -1,c=}$${\displaystyle -30}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-1)}^2-4\cdot 1\cdot (-30)=}$${\displaystyle 1+120=}$${\displaystyle 121}$;

${\displaystyle D>0}$, два корені:

${\displaystyle a_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{1\pm \sqrt{121}}{2}=}$${\displaystyle \frac{1\pm 11}{2}}$;

${\displaystyle a_1=}$${\displaystyle \frac{1+11}{2}=}$${\displaystyle 6}$;

${\displaystyle a_2=}$${\displaystyle \frac{1-11}{2}=}$${\displaystyle -5}$;

${\displaystyle a=}$${\displaystyle 6}$: ${\displaystyle 2+6=}$${\displaystyle 8}$;

${\displaystyle 30:6=}$${\displaystyle 5}$;

${\displaystyle 8-5=}$${\displaystyle 3}$ (при ${\displaystyle a=}$${\displaystyle -5}$: ${\displaystyle b=}$${\displaystyle -3}$;

${\displaystyle c=}$${\displaystyle -6}$).