Question

stiind ca x+1/x=3, x apartine R* calculati x la a doua + 1/xla a doua. Raspunsul este:
a)9
b)7
c)1/9
d)-9

Answer 1

(x+1/x)²=x²+2*x*1/x+1/x²= x²+2+1/x²= x²+1/x²+2
3²=x²+1/x²+2
9=x²+1/x²+2
x²+1/x²=9-2=7
raspuns corect b)

Answer 2

x + 1/x = 3 (ridicam la patrat ambele parti !!!)
      ⇵
(x + 1/x)² = 3²
x²+2·x·1/x +1/x² = 9
x² + 1/x² = 9 - 2 = 7 .