Question

if (x+1/x)=4, find the value of (x²+1/x²) and (x⁴+1/x⁴)​

Answer 1

Answer:

Hey buddy,

x + 1/x = 4

Squaring both sides,

(x + 1/x)² = 4²

x² + 1/x² + 2×x×1/x = 16

x² + 1/x² + 2 = 16

x² + 1/x² = 14

Now, again squaring both sides,

(x² + 1/x²)² = 14²

x⁴ + 1/x⁴ + 2×x²×1/x² = 196

x⁴ + 1/x⁴ + 2 = 196

∴ x⁴ + 1/x⁴ = 194

HOPE IT HELPS......... :)

Answer 2

Answer:

 (x²+1/x²) = 4 (x-1)/x , (x⁴+1/x⁴)​

Step-by-step explanation:

1. (x²+1/x²) = (x+1)(x-1)/x(x)

   (x²+1/x²) = 4 (x-1)/x

2. (x⁴+1/x⁴)​ = (x+1)(x-1)(x+1)(x-1)(x+1)(x-1)