`(9+4sqrt(5))^x+(9-4sqrt(5))^x=18`, then find `x^2-1/(x^2)`

If (9+4sqrt(5))^(x)+(9-4sqrt(5))^(x)=18 then the value of x^(2)-(1)/(x^(2))

sqrt(2)x^(2)+9x+4sqrt(2)

If x=9+4sqrt(5) and xy=1 , then find the value of ((1)/(x^(2))+(1)/(y^(2))) .

If x = 9 - 4sqrt(5) , find the value of x^(2) +(1)/(x^(2)) .

If phi(x)=2cos^(-1)((2)/(sqrt(x)))+sin^(-1)((4sqrt(x-4))/(x)), then phi'(9) is equal to

(3x+sqrt(9x^(2)-5))/(3x-sqrt(9x^(2)-5))=5

(1) sqrt(13-x sqrt(10))=sqrt(8)+sqrt(5) then find the value of x,(2) find sqrt(7+4sqrt(3))

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

If sqrt(x) + sqrt(y) = sqrt(5) , Prove that (dy)/(dx) = (-3)/(2) when x= 4" and "y=9 .

Solve: sqrt(4x-9)+sqrt(4x+9)= 5+sqrt7 .