Question

if x+1/x=5 find the value of x⁴+1/x⁴.

Answer 1

x+1/x = 5
(x+1/x)² = x²+1/x²+2
(5)² = x²+1/x²+2
25-2 = x²+1/x² => 23

(x²+1/x²)² = x⁴+1/x⁴+2
(23)² = x⁴+1/x⁴+2
529-2 = x⁴+1/x⁴
527 = x⁴+1/x⁴

hope this helps

Answer 2

527 is the value of x⁴+1/x⁴ if x+1/x=5.

Step-by-step explanation:

Given,

x + 1/x = 5

To find,

Value of x⁴ + 1/x⁴

So,

(x+1/x)² = (x²+1)/(x²+2)

(x²+1)/(x²+2) = (5)²  

(x²+1)/x² = 25 - 2 => 23

(x²+1/x²)² = x⁴+1/x⁴+2

(x⁴+1)/(x⁴+2) = (23)²  

(x⁴+1)/x⁴ = 529 - 2  

(x⁴+1)/x⁴ = 527

Learn more: find the value of x

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