Question

Cine ma ajuta si pe mn cu 3 probleme la algebra??
Se stie ca x+1/x=2. Calculati: a) x²+1/x² ; b) x²+1/x³ ; c) x⁴+1/x⁴
AJUTATIMA VA ROG !! DAU CEL MAI BUN!!

Answer 1

      
$\frac{x+1}{x}=2 \\ x+1=2x \\ 2x-x=1 \\ x=\boxed{1} \\ \\ a)\;\;\; \frac{ x^{2} +1}{ x^{2}}= \frac{ 1^{2} +1}{1^{2}}= \frac{ 1 +1}{1}=\frac{2}{1}=2 \\ \\ b)\;\;\; \frac{ x^{3} +1}{ x^{3}}= \frac{ 1^{3} +1}{1^{3}}= \frac{ 1 +1}{1}=\frac{2}{1}=2 \\ \\ c)\;\;\; \frac{ x^{4} +1}{ x^{4}}= \frac{ 1^{4} +1}{1^{4}}= \frac{ 1 +1}{1}=\frac{2}{1}=2$