Question

17 PUNCTE+CORONITA SI MULTUMESC:
Calculati x^2+1/x^2 stiind ca x-1/x=3
REPEDE

Answer 1

x -1 /x=3  ridicam la puterea 2
x² - 2·x · 1/x + 1 /x² = 9 
          ↓
          x·1/x =1
x² -2·1 +1 /x² =9
x² +1/x² =9 +2
x² +1/x² =11

Answer 2

$\rm x- \frac{1}{x}=3 \\ \\ x^2+\frac{1}{x^2}=? \\ \\ (x- \frac{1}{x})^2=x^2+( \frac{1}{x})^2-2\cdot \frac{1}{\not x}\cdot\not x \\ \\ 3^2=x^2+\frac{1}{x^2}-2 \\ \\ x^2+\frac{1}{x^2}=9+2 \\ \\ \boxed{\bold{x^2+\frac{1}{x^2}}=11}}$