412 Вправа 412Алгебра 8 клас Тарасенкова 2025 · § 10 · стор. 113

412. Обчисліть x² + x⁻², якщо:

1) ${\displaystyle x+x^{-1}=}$${\displaystyle 3}$; ${\displaystyle {(x+x^{-1})}^2=}$${\displaystyle x^2+2+x^{-2}=}$${\displaystyle 9}$; ${\displaystyle x^2+x^{-2}=}$${\displaystyle 9-2=}$${\displaystyle 7}$;

2) ${\displaystyle x-\frac{1}{x}=}$${\displaystyle 9}$; ${\displaystyle {(x-x^{-1})}^2=}$${\displaystyle x^2-2+x^{-2}=}$${\displaystyle 81}$; ${\displaystyle x^2+x^{-2}=}$${\displaystyle 81+2=}$${\displaystyle 83}$.