Question

x+1/x=2 then x^5+1/x^5=?
(x+1/x=2 then x⁵+1/x⁵=?)

Answer 1

$\huge\boxed{Answer}$

x + 1/x = 2 -------(1)

x² + 1/x² + 2 = 4

x² + 1/x² = 2 -------(2)

Doing Cube of eq. (1)

x³ + 1/x³ + 3(x + 1/x) = 8

x³ + 1/x³ + 3(2) = 8

x³ + 1/x³ + 6 = 8

x³ + 1/x³ = 2 -------(3)

From eq. (2) × eq.(3)

(x² + 1/x²) * (x³ + 1/x³) = 4

x⁵ + x + 1/x + 1/x⁵ = 4

x⁵ + (x + 1/x) + 1/x⁵ = 4

x⁵ + 1/x⁵ + 2 = 4

x⁵ + 1/x⁵ = 2

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{red}{Question}}}}$

x+1/x=2 then x^5+1/x^5=?

(x+1/x=2 then x⁵+1/x⁵=?)

$\huge{\bold{\star{\fcolorbox{black}{red}{Answer}}}}$

x + 1/x = 2 -------(1)

x² + 1/x² + 2 = 4

x² + 1/x² = 2 -------(2)

Doing Cube of eq. (1)

x³ + 1/x³ + 3(x + 1/x) = 8

x³ + 1/x³ + 3(2) = 8

x³ + 1/x³ + 6 = 8

x³ + 1/x³ = 2 -------(3)

From eq. (2) × eq.(3)

(x² + 1/x²) * (x³ + 1/x³) = 4

x⁵ + x + 1/x + 1/x⁵ = 4

x⁵ + (x + 1/x) + 1/x⁵ = 4

x⁵ + 1/x⁵ + 2 = 4

x⁵ + 1/x⁵ = 2