733 Вправа 733Алгебра 8 клас Тарасенкова 2025 · § 17 · стор. 216

733. Розв’яжіть способом виділення квадрата двочлена зведене квадратне рівняння:

1) ${\displaystyle x^2+10x+24=}$${\displaystyle 0}$;

${\displaystyle (x^2+2\cdot x\cdot 5+5^2)-25+24=}$${\displaystyle 0}$;

${\displaystyle {(x+5)}^2-1=}$${\displaystyle 0}$;

${\displaystyle {(x+5)}^2=}$${\displaystyle 1}$;

${\displaystyle x+5=}$${\displaystyle \sqrt{1}}$ або ${\displaystyle x+5=}$${\displaystyle -\sqrt{1}}$;

${\displaystyle x+5=}$${\displaystyle 1}$ або ${\displaystyle x+5=}$${\displaystyle -1}$;

${\displaystyle x=}$${\displaystyle 1-5}$ або ${\displaystyle x=}$${\displaystyle -1-5}$;

${\displaystyle x=}$${\displaystyle -4}$ або ${\displaystyle x=}$${\displaystyle -6}$;

2) ${\displaystyle x^2+2x-8=}$${\displaystyle 0}$;

${\displaystyle (x^2+2\cdot x\cdot 1+1^2)-1-8=}$${\displaystyle 0}$;

${\displaystyle {(x+1)}^2-9=}$${\displaystyle 0}$;

${\displaystyle {(x+1)}^2=}$${\displaystyle 9}$;

${\displaystyle x+1=}$${\displaystyle \sqrt{9}}$ або ${\displaystyle x+1=}$${\displaystyle -\sqrt{9}}$;

${\displaystyle x+1=}$${\displaystyle 3}$ або ${\displaystyle x+1=}$${\displaystyle -3}$;

${\displaystyle x=}$${\displaystyle 3-1}$ або ${\displaystyle x=}$${\displaystyle -3-1}$;

${\displaystyle x=}$${\displaystyle 2}$ або ${\displaystyle x=}$${\displaystyle -4}$;

3) ${\displaystyle x^2-8x+16=}$${\displaystyle 0}$;

${\displaystyle {(x-4)}^2=}$${\displaystyle 0}$;

${\displaystyle x-4=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 4}$.