" If "x=(1)/(sqrt(3)+2)," then "(x+(1)/(x))^(2)=

If x=(1)/(sqrt(3)-sqrt(2)) find x+(1)/(x)

If x +(1)/(x) = 2sqrt(3) , then x^(2) + (1)/(x^(2)) is equal to .

If x + (1)/(x) = 3 sqrt(2) , then x^(2) + (1)/(x^(2)) is equal to :

y(x)=cos(3cos^(-1)x),x in[-1,1],x!=+-(sqrt(3))/(2) Then (1)/(y(x)){(x^(2)-1)(d^(2)y(x))/(dx^(2))+x(dy(x))/(dx)} equals

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=