If `a=1/(a-5)` then the value of `a+1/a`

If a + (1)/(a) =3, then the value of a ^(5) + (1)/(a ^(5)) is:

If 5a+ (1)/(3a) = 5 , then the value of 9a^(2)+(1)/(25a^(2)) is

If sin^(16) alpha = (1)/(5) , then the value of (1)/( cos^(2) alpha) + (1)/( 1 + sin^(2) alpha) + (2)/( 1 + sin^(4) alpha) + (4)/( 1 + sin^(8) alpha) is

If x+1/(x)=5 , then the value of x^(2)+1/(x^(2)) is:

If alpha is a non-real and alpha=(1)^(1//5) then the value of 2^(|1+alpha+alpha^2+alpha^(-2) +alpha^(-1)|) is equal to

Let g(x) be differentiable function on R such f(x)=g(x)ln(4x^(3)-x)andg'((1)/(3))=-5 then the value of f' ((1)/(3)) is equal to