669 Вправа 669Алгебра 8 клас Бевз 2025 · § 13 · стор. 129

669. Розв’яжи рівняння.

За означенням: якщо ${\displaystyle \sqrt{A}=}$${\displaystyle m}$, ${\displaystyle m\ge 0}$, то ${\displaystyle A=}$${\displaystyle m^2}$.

а) ${\displaystyle \sqrt{x+3}=}$${\displaystyle 5}$;

${\displaystyle x+3=}$${\displaystyle 5^2}$;

${\displaystyle x+3=}$${\displaystyle 25}$;

${\displaystyle x=}$${\displaystyle 25-3}$;

${\displaystyle x=}$${\displaystyle 22}$;

б) ${\displaystyle \sqrt{11-y}=}$${\displaystyle 7}$;

${\displaystyle 11-y=}$${\displaystyle 7^2}$;

${\displaystyle 11-y=}$${\displaystyle 49}$;

${\displaystyle -y=}$${\displaystyle 49-11}$;

${\displaystyle -y=}$${\displaystyle 38}$;

${\displaystyle y=}$${\displaystyle -38}$;

в) ${\displaystyle \sqrt{5x-1}=}$${\displaystyle 3}$;

${\displaystyle 5x-1=}$${\displaystyle 3^2}$;

${\displaystyle 5x-1=}$${\displaystyle 9}$;

${\displaystyle 5x=}$${\displaystyle 10}$;

${\displaystyle x=}$${\displaystyle 10:5}$;

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

г) ${\displaystyle \sqrt{1+2x}=}$${\displaystyle 5}$;

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

${\displaystyle 1+2x=}$${\displaystyle 25}$;

${\displaystyle 2x=}$${\displaystyle 24}$;

${\displaystyle x=}$${\displaystyle 24:2}$;

${\displaystyle x=}$${\displaystyle 12}$;

ґ) ${\displaystyle \frac{12}{\sqrt{x+2}}=}$${\displaystyle 3}$;

${\displaystyle \sqrt{x+2}=}$${\displaystyle 12:3}$;

${\displaystyle \sqrt{x+2}=}$${\displaystyle 4}$;

${\displaystyle x+2=}$${\displaystyle 4^2}$;

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

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

${\displaystyle x=}$${\displaystyle 14}$;

д) ${\displaystyle \frac{28}{\sqrt{x+5}}=}$${\displaystyle 7}$;

${\displaystyle \sqrt{x+5}=}$${\displaystyle 28:7}$;

${\displaystyle \sqrt{x+5}=}$${\displaystyle 4}$;

${\displaystyle x+5=}$${\displaystyle 4^2}$;

${\displaystyle x+5=}$${\displaystyle 16}$;

${\displaystyle x=}$${\displaystyle 16-5}$;

${\displaystyle x=}$${\displaystyle 11}$.