962 Вправа 962Алгебра 8 клас Бевз 2025 · § 19 · стор. 183

962. Користуючись формулою коренів, розв’яжи рівняння. а) 6x² − 12,5x + 6 = 0; б) 8x² − 8,8x + 2,1 = 0.

Спочатку позбудемося десяткових дробів.

а) ${\displaystyle 6x^2-12,5x+6=}$${\displaystyle 0\mid \cdot 2}$;

${\displaystyle 12x^2-25x+12=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 12,b=}$${\displaystyle -25,c=}$${\displaystyle 12}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-25)}^2-4\cdot 12\cdot 12=}$${\displaystyle 625-576=}$${\displaystyle 49}$;

${\displaystyle D>0}$, два корені:

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{25\pm \sqrt{49}}{24}=}$${\displaystyle \frac{25\pm 7}{24}}$;

${\displaystyle x_1=}$${\displaystyle \frac{25+7}{24}=}$${\displaystyle \frac{4}{3}}$;

${\displaystyle x_2=}$${\displaystyle \frac{25-7}{24}=}$${\displaystyle 0,75}$;

б) ${\displaystyle 8x^2-8,8x+2,1=}$${\displaystyle 0\mid \cdot 10}$;

${\displaystyle 80x^2-88x+21=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 80,b=}$${\displaystyle -88,c=}$${\displaystyle 21}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-88)}^2-4\cdot 80\cdot 21=}$${\displaystyle 7744-6720=}$${\displaystyle 1024}$;

${\displaystyle D>0}$, два корені:

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{88\pm \sqrt{1024}}{160}=}$${\displaystyle \frac{88\pm 32}{160}}$;

${\displaystyle x_1=}$${\displaystyle \frac{88+32}{160}=}$${\displaystyle 0,75}$;

${\displaystyle x_2=}$${\displaystyle \frac{88-32}{160}=}$${\displaystyle 0,35}$.