Question

calculati x^2 +1/x^2 stiind ca x+1/x=9 unde x apartine R

Answer 1

   
[tex]\displaystyle\\ \frac{x+1}{x}= 9\\\\ x+1 = 9x\\\\ 9x-x=1\\\\ 8x=1\\\\ x = \frac{1}{8} \\\\ \frac{x^2+1}{x^2}= \frac{\left(\frac{1}{8} \right)^2+1}{\left(\frac{1}{8} \right)^2}= \frac{\frac{1}{64} +1}{\frac{1}{64}}= \frac{\frac{64+1}{64}}{\frac{1}{64}}= \frac{\frac{65}{64}}{\frac{1}{64}}=\frac{65}{64}\cdot \frac{64}{1}= \frac{65}{1}=\boxed{65}[/tex]