916 Вправа 916Алгебра 8 клас Бевз 2025 · § 18 · стор. 174

916. Розв’яжи рівняння.

а) ${\displaystyle {(x+2)}^2+(x+10)(x-2)=}$${\displaystyle x(x+12)}$;

${\displaystyle x^2+4x+4+x^2+8x-20=}$${\displaystyle x^2+12x}$;

${\displaystyle 2x^2+12x-16=}$${\displaystyle x^2+12x}$;

${\displaystyle x^2=}$${\displaystyle 16}$;

${\displaystyle x=}$${\displaystyle \pm 4}$;

б) ${\displaystyle (x+6)(x+1)-{(x+5)}^2=}$${\displaystyle x^2-19}$;

${\displaystyle x^2+7x+6-x^2-10x-25=}$${\displaystyle x^2-19}$;

${\displaystyle -3x-19=}$${\displaystyle x^2-19}$;

${\displaystyle x^2+3x=}$${\displaystyle 0}$;

${\displaystyle x(x+3)=}$${\displaystyle 0}$;

${\displaystyle x_1=}$${\displaystyle 0,x_2=}$${\displaystyle -3}$;

в) ${\displaystyle {(x-2)}^2+{(x+1)}^2=}$${\displaystyle (x+3)(x-1)+8}$;

${\displaystyle x^2-4x+4+x^2+2x+1=}$${\displaystyle x^2+2x-3+8}$;

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

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

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

${\displaystyle x_1=}$${\displaystyle 0,x_2=}$${\displaystyle 4}$.