" 6.(i) If "x=1+sqrt(2)," then show that: "(x-(1)/(x))^(3)=8

If x=1/sqrt2(1+i) then show that x^6+x^4+x^2+1=0

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

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

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=3+sqrt(8), then x^(2)+(1)/(x^(2)) will be

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 2x=-1+sqrt(3)i , then the value of (1-x^(2)+x)^(6)-(1-x+x^(2))^(6)=

If 2 x =-1 + I sqrt(3) then the value of (1-x^(2) +x)^(6) - (1-x+x^(2))^(6)=

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