Question

stiind ca x+1/x=7/3 unde x este nr real nenul aratati ca x²+1/x²=31/9
va rog sa ma ajutati urgent ofer 50 de puncte​

Answer 1

$\displaystyle\bf\\x+\frac{1}{x}=\frac{7}{3}~|^2 \implies (x+\frac{1}{x})^2=\frac{49}{9} \Leftrightarrow x^2+2+\frac{1}{x^2} =\frac{49}{9} \Leftrightarrow x^2 + \frac{1}{x^{2}}=\frac{49}{9}-2=\\\frac{49-18}{9} =\frac{31}{9},~\forall x \in \mathbb{R^*}.$