Question

If x+1/x=9,find the value of x²+1/x²and x⁴+1/x⁴.​

Answer 1

Answer:

Step-by-step explanation:

1)  x + 1/x = 9

  (x + 1/x) sq. = x² + 1/x² + 2

   9 = x² + 1/x² + 2

   9 - 2 = x² + 1/x²

Hence, x²+1/x² = 7

2)  x² + 1/x² = 7

    (x² + 1/x²)² = (x²)² + (1/x²)² + 2

     7²  =  x⁴ + 1/x⁴ + 2

     49 - 2 = x⁴ + 1/x⁴

     47 = x⁴ + 1/x⁴

Hence, x⁴ + 1/x⁴ = 47

Answer 2

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