Question

if x² + 1/x² is 23 , then find value of x³ + 1/x³​

Answer 1

Step-by-step explanation:

x2 + 1/x2 = 23

x2+ 1/x2 + 2= 25

(x+1/x)2 = 25

x+1/x = 5 --- (1)

(x+1/x)3 = 53

x3 + 1/x3 + 3(x+1/x) = 125

Put the value of (1)

x3 + 1/x3 + 3*5 = 125

x3 + 1/x3 = 125 - 15 = 110

Answer 2

Answer:

Solution :-

x² + 1/x² = 23 (1)

x² + 1/x² + 2 = 25

x² + 1/x² + 2 × x × 1/x = 25

Applying Identity

(a + b)² = a² + 2ab + b²

(x + ⅕ )² = 5²

(x + 1/x) = 5 (2)

Now,

By Multiplying

(x² + 1/x²) × (x + 1/x) = (23)(5)

x³ + x + 1/x + 1/x³ = (23)(5)

x³ + x + 1/x + 1/x³ = 115

By mixing like terms

x³ + 1/x³ (x + 1/x) = 115

x³ + 1/x³ + 5 = 115

x³ + 1/x³ = 115 - 5

=> 110