If `x=1+sqrt(2)` ,then show that : `(x-(1)/(x))^(3)=8`

if x=(3-2sqrt(2)) then show that (sqrt(x)+(1)/(sqrt(x)))=+-2

If y= sqrt(x^2+6x+8) , then show that (1+ iy)^(1//2)+(1-iy)^(1//2)= sqrt(2(x+4)) .

If y=(1)/(3)"log" (x+1)/(sqrt(x^(2)-x+1))+(1)/(sqrt(3))"tan"^(-1)(2x-1)/(sqrt(3)) , show that, (dy)/(dx)=(1)/(x^(3)+1)

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(2) .

If x = 3 + sqrt(8) then (x^(2) + (1)/(x^(2)))=?

If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) , then show that (dy)/(dx) = x/(sqrt(1 - x^4))

If 2x = sqrt((a)/(b)) - sqrt((b)/(a)) , then show that (2a sqrt(1 + x^(2)))/(x + sqrt(1 + x^(2))) = a + b

If x=(4+sqrt(15))^(1//3)+(4-sqrt(15))^(1//3) , then show that x^(3)-3x-8=0 .