Question

if x^2- 5x+1=0,then find the value of x^5+1/x^5

Answer 1

=> x^2 + 1 = 5x divide by x
x +1/x = 5 ---- 1 (square on both sides

x ^2 + 1/x^2 =23 -----2
multiply both equations which gives x^3 +1/x^3 +(1/x + x) =115

x^3 + 1/x^3 = 110 ------3

square on both sides 2nd equation

x^4 + 1/x^4 = 527 multiply this equation with 1st equation
x^5 + 1/x^5 + x^3 +1/x^3 = 2635 substitute 3rd equation

x^5 + 1/x^5 = 2525