If `(x+1/x)^2=3` then find the value of `x^(206)+x^(200)+x^(90)+x^(84)+x^(18)+x^(12)+x^8+1`

If 1:3 :: x: 18 then find the value of x.

If (x +1/x) = 2 , then find the value of (x^3 + 1//x^3) + (x^(18) + 1//x^(18))

If x^(2)+(1)/(x^(2))=18 then find the value of x^(3)-(1)/(x^(3))

If x + (1)/(2x)= 3 , find the value of 8x^(3) + (1)/(x^(3))

If x+(1)/(x)=12, find the value of x-(1)/(x)

If x^(2) + ((1)/(x^(2))) =1 , then what is the value of x^(48) + x^(42) + x^(36) + x^(30) + x^(24) + x^(18) + x^(12) + x^(6) + 1 ?