415* Вправа 415Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 113

415. Знайдіть (x/y)², якщо:

1) ${\displaystyle \frac{4x^{-2}+y^{-2}}{x^{-2}+5y^{-2}}=}$${\displaystyle 1}$; ${\displaystyle 4x^{-2}+y^{-2}=}$${\displaystyle x^{-2}+5y^{-2}}$; ${\displaystyle 3x^{-2}=}$${\displaystyle 4y^{-2}}$;

${\displaystyle \frac{3}{x^2}=}$${\displaystyle \frac{4}{y^2}}$; ${\displaystyle \frac{x^2}{y^2}=}$${\displaystyle \frac{3}{4}}$; ${\displaystyle {\left(\frac{x}{y}\right)}^2=}$${\displaystyle 0,75}$;

2) ${\displaystyle x^{-2}+y^{-2}=}$${\displaystyle \frac{2}{x^2}-\frac{3}{y^2}}$; ${\displaystyle x^{-2}+y^{-2}=}$${\displaystyle 2x^{-2}-3y^{-2}}$; ${\displaystyle 4y^{-2}=}$${\displaystyle x^{-2}}$;

${\displaystyle \frac{4}{y^2}=}$${\displaystyle \frac{1}{x^2}}$; ${\displaystyle \frac{x^2}{y^2}=}$${\displaystyle \frac{1}{4}}$; ${\displaystyle {\left(\frac{x}{y}\right)}^2=}$${\displaystyle 0,25}$.