Question

Stiind ca x+1/x=3, x aparține R calculați x*+1/x*
Va rog, am nevoie urgent!
*--> la puterea a doua

Answer 1

   
[tex]\displaystyle \\ \texttt{Se da: }x+ \frac{1}{x} = 3 \\ \\ \texttt{Se cere: } x^2+ \frac{1}{x^2} = ? \\ \\ \texttt{Rezolvare: } \\ \\ x+ \frac{1}{x} = 3 ~~~~~| \text{Ridicam la puterea a 2-a.} \\ \\ \left(x+ \frac{1}{x} \right)^2= 3^2 \\ \\ \left(x+ \frac{1}{x} \right)^2= 9 \\ \\ x^2 + 2 \cdot x \cdot \frac{1}{x} + \left(\frac{1}{x}\right)^2 = 9 \\ \\ x^2 + \frac{2x}{x} + \left(\frac{1}{x}\right)^2 = 9 \\ \\ x^2 + 2+ \frac{1}{x^2} = 9 \\ \\ x^2 + \frac{1}{x^2} = 9-2 [/tex]

[tex]\displaystyle \\ \boxed{x^2 + \frac{1}{x^2} = 7 } [/tex]