If `x^2+1=sqrt(3)x ,` then `(x^3+1/(x^3))^(2n+1)` for any `n in NN` is equal to

If 1+x^(2)=sqrt(3)x , then sum_(n=1)^(24)(x^(n)-(1)/(x^n))^(2) is equal to

If 1+x^(2)=sqrt(3)x, then sum_(n=1)^(24)(x^(n)-(1)/(x^(n))) is equal to

If 1+x^(2)=sqrt(3)x , then sum_(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

If x lt -(1)/sqrt(3) , then tan^(-1)(3x-x^(3))/(1-3x^(2)) equals

If x gt (1)/sqrt(3) then tan^(-1) (3x-x^(3))/(1-3x^(2)) equals

If there is a term independent of x in (x+(1)/(x^(2)))^(n) ,show that it is equal to (n!)/(((n)/(3))!((2n)/(3))!)

If x_0=1 and x_(n+1)=3sqrt(2x_(n)), then x_3 =

If there is a term independent of x in ( x+1/x^2)^n , show that it is equal to (n!)/((n/3)! ((2n)/3)! )