735 Вправа 735Алгебра 8 клас Тарасенкова 2025 · § 17 · стор. 216

735. Розв’яжіть способом виділення квадрата двочлена рівняння:

1) ${\displaystyle x^2+5x-14=}$${\displaystyle 0}$;

${\displaystyle (x^2+2\cdot x\cdot 2,5+{2,5}^2)-6,25-14=}$${\displaystyle 0}$;

${\displaystyle {(x+2,5)}^2-20,25=}$${\displaystyle 0}$;

${\displaystyle {(x+2,5)}^2=}$${\displaystyle 20,25}$;

${\displaystyle x+2,5=}$${\displaystyle \sqrt{20,25}}$ або ${\displaystyle x+2,5=}$${\displaystyle -\sqrt{20,25}}$;

${\displaystyle x+2,5=}$${\displaystyle 4,5}$ або ${\displaystyle x+2,5=}$${\displaystyle -4,5}$;

${\displaystyle x=}$${\displaystyle 4,5-2,5}$ або ${\displaystyle x=}$${\displaystyle -4,5-2,5}$;

${\displaystyle x=}$${\displaystyle 2}$ або ${\displaystyle x=}$${\displaystyle -7}$;

2) ${\displaystyle x^2-3x-10=}$${\displaystyle 0}$;

${\displaystyle (x^2-2\cdot x\cdot 1,5+{1,5}^2)-2,25-10=}$${\displaystyle 0}$;

${\displaystyle {(x-1,5)}^2-12,25=}$${\displaystyle 0}$;

${\displaystyle {(x-1,5)}^2=}$${\displaystyle 12,25}$;

${\displaystyle x-1,5=}$${\displaystyle \sqrt{12,25}}$ або ${\displaystyle x-1,5=}$${\displaystyle -\sqrt{12,25}}$;

${\displaystyle x-1,5=}$${\displaystyle 3,5}$ або ${\displaystyle x-1,5=}$${\displaystyle -3,5}$;

${\displaystyle x=}$${\displaystyle 3,5+1,5}$ або ${\displaystyle x=}$${\displaystyle -3,5+1,5}$;

${\displaystyle x=}$${\displaystyle 5}$ або ${\displaystyle x=}$${\displaystyle -2}$;

3) ${\displaystyle 2x^2-3x+1=}$${\displaystyle 0}$ | ${\displaystyle :2}$

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

${\displaystyle (x^2-2\cdot x\cdot 0,75+{0,75}^2)-0,5625+0,5=}$${\displaystyle 0}$;

${\displaystyle {(x-0,75)}^2-0,0625=}$${\displaystyle 0}$;

${\displaystyle {(x-0,75)}^2=}$${\displaystyle 0,0625}$;

${\displaystyle x-0,75=}$${\displaystyle \sqrt{0,0625}}$ або ${\displaystyle x-0,75=}$${\displaystyle -\sqrt{0,0625}}$;

${\displaystyle x-0,75=}$${\displaystyle 0,25}$ або ${\displaystyle x-0,75=}$${\displaystyle -0,25}$;

${\displaystyle x=}$${\displaystyle 0,25+0,75}$ або ${\displaystyle x=}$${\displaystyle -0,25+0,75}$;

${\displaystyle x=}$${\displaystyle 1}$ або ${\displaystyle x=}$${\displaystyle 0,5}$.