Question

x+1/x=a then x^4+ 1/x^4= a^4-4a^2+2

Answer 1

x+1/x =a

square on both sides,

(x+1/x)^2 =a^2

x^2 +1/x^2 + 2(x*1/x) =a^2

x^2+1/x^2 =a^2 -2

again square on both sides,

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

x^4 +1/x^4 +2(x^2 *1/x^2) = (a^2-2)^2

x^4+1/x^4 =(a^2 -2)^2 -2

x^4 +1/x^4 = a^4 +4 -4a -2

x^4 +1/x^4 = a^4 -4a+2