if x + 1/x = 2 , then what is the value of x⁹⁵ + 1/x⁹⁵.

x + 1/x = 2

x² + 1/x² + 2 = 4

Therefore, x² + 1/x² = 2

x⁴ + 1/x⁴ + 2 = 4

x⁴ + 1/x⁴ = 2

Similarly, x⁸ + 1/x⁸ = 2

So, x³² + 1/x³² = 2

Thus, x⁶⁴ + 1/x⁶⁴ = 2

Now, (x³¹ + 1/x³¹)(x⁶⁴ + 1/x⁶⁴)= x⁹⁵ + 1/x³³ + x³³ + 1/x⁹⁵

x⁹⁵ + 1/x⁹⁵ = (x³¹ + 1/x³¹)(x⁶⁴ + 1/x⁶⁴) - (1/x³³ + x³³)