Question

if x+1/x=5,find the value of x⁴+1/x⁴​

Answer 1

Answer:

x⁴ + 1/x⁴ = 527

Step-by-step explanation:

x + 1/x = 5

On Squaring on both sides,

(x + 1/x)² = (5)²

x² + 2×x×1/x + 1/x² = 25                                            (By using (a+b)² identity)

x² + 2 + 1/x² = 25                                                      (Both the x gets cancelled)

x² + 1/x² = 25 - 2

x² + 1/x² = 23  ----------------------------------(1)

Now squaring on both sides again

(x² + 1/x²)² = (23)²

x⁴ + 2×x²×1/x² + 1/x⁴ = 529

x⁴ + 1/x⁴ = 529 - 2

x⁴ + 1/x⁴ = 527

Answer 2

Step-by-step explanation:

find value of x⁴ + 1/x⁴

so,

(x+1/x)² = (x²+1)/(x²+ 2)

(x²+1)/(x²+2) = 5²

(x²+1)/x² = 25-2

= 23

(x² + 1/x²)² = x⁴+1/x⁴+2

(x⁴ + 1)/(x⁴+2)=23²

(x⁴+1)/x⁴ = 529 - 2

= 527