`x^(3)-(1)/(x^(3))` if `"x^(2)+(1)/(x^(2))=18`

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))

x^(3)+x^(2)-(1)/(x^(2))+(1)/(x^(3))=

Find the term independent of x (constant term) in the following expansion: (i) (x^(2)-(1)/(3x))^(9) " "(ii) (x-(1)/(x))^(10) (iii) (3x-(2)/(x^(2)))^(18) " "(iv) (1)/(x^(n))(1+x)^(2n) (V)(3sqrt(x)+(1)/(2(3sqrt(x))))^(18)" "(vi)((3x^(2))/(2)-(1)/(3x))^(6)

((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))=

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^(2))) where |x|<(1)/(sqrt(3))* Then a value of y is : (1)(3x-x^(3))/(1-3x^(2))(2)(3x+x^(3))/(1-3x^(2))(3)(3x-x^(3))/(1+3x^(2))(4)(3x+x^(3))/(1+3x^(2))

(i) (2x+3) (3x-5) (ii) x(1+x)^(3) (iii) (sqrtx + 1/x) (x -1/sqrtx) (iv) (x-1/x)^(2) (v) (x^(2) + 1/x^(2))^(3) (vi) (2x^(2) +5x-1) (x-3)

(x^((1)/(3))+(1)/(2*x^((1)/(3))))^(18)

If x=2 - 2^((1)/(3)) + 2^((2)/(3)) find the value of x^(3)-6x^(2) + 18x + 18

x=3+3^((2)/(3))+3^((1)/(3)) then the value of x^(3)-9x^(2)+18x-12is