963 Вправа 963Алгебра 8 клас Бевз 2025 · § 19 · стор. 183

963. Користуючись формулою коренів, розв’яжи рівняння. а) 10y² − 0,8y = 1,92; б) 4n² + 11n + 7,36 = 0.

а) ${\displaystyle 10y^2-0,8y=}$${\displaystyle 1,92}$;

${\displaystyle 10y^2-0,8y-1,92=}$${\displaystyle 0\mid \cdot 100}$;

${\displaystyle 1000y^2-80y-192=}$${\displaystyle 0\mid :8}$;

${\displaystyle 125y^2-10y-24=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 125,b=}$${\displaystyle -10,c=}$${\displaystyle -24}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-10)}^2-4\cdot 125\cdot (-24)=}$${\displaystyle 100+12000=}$${\displaystyle 12100}$;

${\displaystyle D>0}$, два корені:

${\displaystyle y_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{10\pm \sqrt{12100}}{250}=}$${\displaystyle \frac{10\pm 110}{250}}$;

${\displaystyle y_1=}$${\displaystyle \frac{10+110}{250}=}$${\displaystyle 0,48}$;

${\displaystyle y_2=}$${\displaystyle \frac{10-110}{250}=}$${\displaystyle -0,4}$;

б) ${\displaystyle 4n^2+11n+7,36=}$${\displaystyle 0\mid \cdot 25}$;

${\displaystyle 100n^2+275n+184=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 100,b=}$${\displaystyle 275,c=}$${\displaystyle 184}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle 275^2-4\cdot 100\cdot 184=}$${\displaystyle 75625-73600=}$${\displaystyle 2025}$;

${\displaystyle D>0}$, два корені:

${\displaystyle n_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{-275\pm \sqrt{2025}}{200}=}$${\displaystyle \frac{-275\pm 45}{200}}$;

${\displaystyle n_1=}$${\displaystyle \frac{-275+45}{200}=}$${\displaystyle -1,15}$;

${\displaystyle n_2=}$${\displaystyle \frac{-275-45}{200}=}$${\displaystyle -1,6}$.