Correct Option: A

x + 1/x = 3 ........................ (i)
On squaring both side, we will get
(x + 1/x)² = (3)²
Use the Square algebra formula (a + b)² = a² + 2ab + b²
⇒ x² + 1/x² + 2 = 9
⇒ x² + 1/x² = 7 ..................(ii)
Again squaring both sides, we will get
(x² + 1/x²)² = (7)²
Use the Square algebra formula (a + b)² = a² + 2ab + b²
⇒ x⁴ + 1/⁴ + 2 = 49
⇒ x⁴ + 1/x⁴ = 47 .....................(iii)
On cubing the equation (i) both side, we will get
(x + 1/x)³ = (3)³
Use the cube algebra formula (a + b)³ = a³ + 3a²b + 3ab² + b³
⇒ x³+ 1/x³ + 3(x + 1/x) = 27
⇒ x³ + 1/x³ + 9 = 27 [∴ (x + 1/x) = 3]
⇒ x³ + 1/x³ = 18 ...................(iv)
On multiplying Eqs. (i) and (iii) , we get
∴ (x⁴ + 1/x⁴) (x + 1/x) = 47 x 3
⇒ x⁵ + 1/x⁵ + x³ + 1/x³ = 141
⇒ x⁵ + 1/x⁵ + 18 = 141 [from Eq. (iv)]
⇒ x⁵ + 1/x⁵ = 123