Question

please answer fast
If x+1/x=5,then find the value of
(1) x$^{2}$+1/x$^{2}$
(2)x$^{4}$+1/x$^{4}$

Answer 1

x + 1/x = 5

Squaring on both sides

( x + 1/x )² = 5²

Using algebraic identity (a + b)² = a² + b² + 2ab

x² + 1/x² + 2( x)( 1/x ) = 25

x² + 1/x² + 2 = 25

x² + 1/x² = 25 - 2 = 23

Squaring on both sides

( x² + 1/x² )² = 23²

Using algebraic identity (a + b)² = a² + b² + 2ab

( x² )² + ( 1/x² )² + 2( x² )( 1/x² ) = 529

x⁴ + 1/x⁴ + 2 = 529

x⁴ + 1/x⁴ = 529 - 2 = 527