Question

x^4+1/x^4=194 find x+1/x,x^3+1/x^3,x^2+1/x^2,x-1/x,x^3-1/x^3

Answer 1

x^4 + 1 /x^4 = 194

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

-2 (x^2) (1 / x^2) = 194 .

(x^2 + 1 / x^2) ^2 - 2 = 194

(x^2 + 1 / x^2 ) ^2 = 196.

x^2 + 1 / x^2 = √196

x^2 + 1 / x^2 = 14

(x) ^2 + 1 / (x) ^2 + 2 (x) (1 /x) - 2(x) (1 /x) =14

(x + 1 / x )^2 - 2 = 14.

(x + 1/x )^2 =16

x + 1 / x = 4

hence, x + 1 /x = 4, x^2 + 1/ x^2 = 14.

now other terms you could find by yourself in the same manner.

hope it helps !
thank you !