Question

If x +1/x=4 find the value of 1) x square +1/x square 2) x to the power 4 +1/x to the power 4 3) x cube+1/x cube​

Answer 1

Answer:

Step-by-step explanation:

1)  (x+1/x)² = 4²

  ∴  x² + 1/x² +2 = 16

  ∴ x² + 1/x² = 16 - 2 = 14

2) (x² + 1/x²)² = 14²

  ∴ x⁴ + 1/x⁴ + 2 = 196

  ∴ x⁴ + 1/x⁴ = 196 - 2= 194

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

 ∴  4³ = x³ + 1/x³ + 3  x  4

 ∴ 64 - 12 = x³ + 1/x³

∴x³ + 1/x³  =  52