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If (x+1/x) = 6, what is the value of x⁵ + 1/x⁵ = ?

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If (x+1/x) = 6, what is the value of x⁵ + 1/x⁵ = ?

Step-by-step explanation:  x + 1/x = 5 ( given )

So,

x + 1/x = 5 …(1)

Squaring both sides

( x+1/x)² = 5²

x² + 1/x² + 2  =25

x² + 1/x² = 25 – 2

x² + 1/x ² = 23  ….(2)

Cube of the equation

x³ + 1/x³ = ( x+ 1/x )³ – 3 (x +1/x)

x³ + 1/x ³ = (5)³ – 3 (5)

x³ + 1/x³ = 125 -15

x³ + 1/x³ = 110 …(3)

Now taking all equation

(x² + 1/x² ) (x³ + 1/x³ ) = (x⁵ +1/x +x + 1/x⁵)

23 ₓ 110 = x⁵ + 1/x⁵

2530 = x⁵ + 1/x⁵

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