471 Вправа 471Алгебра 8 клас Бевз 2025 · § 9 · стор. 93

471. Розв’яжи рівняння.

а) ${\displaystyle 2x^{-1}-x^{-1}=}$${\displaystyle 2}$;

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

${\displaystyle \frac{1}{x}=}$${\displaystyle 2}$;

${\displaystyle x=}$${\displaystyle 0,5}$;

б) ${\displaystyle x^{-2}-x^{-1}=}$${\displaystyle 0}$;

${\displaystyle \frac{1}{x^2}-\frac{1}{x}=}$${\displaystyle 0}$;

${\displaystyle \frac{1-x}{x^2}=}$${\displaystyle 0}$;

${\displaystyle \{\begin{array}{rl}& 1-x=0,\\ & x\ne 0;\end{array}}$ ${\displaystyle x=}$${\displaystyle 1}$;

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

${\displaystyle \frac{2x-1}{x}=}$${\displaystyle x}$;

${\displaystyle x\ne 0}$;

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

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

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

${\displaystyle x=}$${\displaystyle 1}$.