Question

Stind ca x+1/x=3 ,x € R* calculati x*2 +1/x*2

Answer 1

$\displaystyle x+ \frac{1}{x}=3 \Rightarrow \left( x+ \frac{1}{x}\right)^2=9 \Leftrightarrow x^2+2 \cdot x \cdot \frac{1}{x}+ \frac{1}{x^2}=9 \Leftrightarrow \\ \\ x^2+2+ \frac{1}{x^2}=9 \Rightarrow \boxed{x^2+ \frac{1}{x^2}=7}~.$

Answer 2

x + 1/x = 3    ridicam la puterea a 2-a ambele parti ...
(x+1/x)² = 3²
         ↓
x² + 2*x*1/x +1/x² = 9
    
    x²  +  1/x² = 9 - 2 = 7