If `x=sqrt5+2` , then find the value of `x^2+1/x^2`

If (x^(+(1)/(2)) + x^(-(1)/(2)))^(2) = (9)/(2) , then find the value of (x^((1)/(2))-x^(-(1)/(2))) for x gt 1 .

If x^(2) + (1)/(x^(2)) = 23 , then find the value of x + (1)/( x) and x^(3) + (1)/( x^(3))

If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

If the locus of the moving poin P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a.

If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 is ____________

If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 is ____________

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

If (x^(1//2)+x^(-1//2))^(2)=9/2 find the value of (x^(1//2)-x^(-1//2)) for x gt 1