If `x=3sqrta+1/(3sqrta)` then find `x^3-3x.`

If x=sqrta+(1)/(sqrta), y=sqrta-(1)/(sqrta) then the value of x^(4)+y^(4)-2x^(2)y^(2) is

If 2x = sqrta+1/sqrta . Show that sqrt(x^2-1)/(x-sqrt(x^2-1))(a-1)

If f(x)=a^x/(a^x+sqrta) then f(x)+f(1-x)=

If x+(1)/(x)=7 ,then find x^(3)-(1)/(x^(3))

If x+(1)/(x)=7 ,then find x^(3)-(1)/(x^(3))

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

If sqrta : sqrtb = sqrt3 : sqrt2 " and " sqrtb : sqrtc = sqrt3 : sqrt2 , then find the value of (sqrta + sqrtb ) : ( sqrtb + sqrtc) .

Prove that lim_(x to 0) (sqrt(a+x)-sqrta)/x = 1/(2sqrta) ( a ne o)