If `y-1/y` =`3-2sqrt2` find `y^3-1/y^3`

If y=2+sqrt(3) ,find the value of y^(2)+(1)/(Y^(2))

The complex numbrs x and y such that x,x+2y,2x+y are n A.P. and (y+1)^2, xy+5, (x+1)^2 are in G.P. are (A) x=3, y=1 (B) x=-1+2sqrt(2)i, y=1/3 (-1+2sqrt(2)i) (C) x=sqrt(2)+i, y=3sqrt(5)-sqrt(2)i (D) x=-1(1+2sqrt(2)i), y= - 1/3 (1+2sqrt(2)i)

If (2x + 3,y-1) =(3,5) , then find x and y.

If 3^(49)(x+i y)=(3/2+(sqrt(3))/2i)^(100) and x=k y then k is: a. -1//3 b. sqrt(3) c. -sqrt(3) d. -1/(sqrt(3))

If angle between the line (x-2)/1=(y-3)/2=(z+5)/(-2) and 2x-y-kz=lambda is cos^-1 ((2sqrt2)/3) then find k (A) sqrt(3/5) (B) 3/sqrt5 (C) sqrt5/3 (D) sqrt(5/3)

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) , find x^2+y^2

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) , find x^2+y^2

If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) find x^2+y^2

Find the area bounded by the curves y=sqrt(1-x^(2)) and y=x^(3)-x without using integration.

Find the angle between the following pairs of lines : (i) y=sqrt(3)x+1 and y=(1)/(sqrt(3))x+2 (ii) y=x and y=1-x (iii) 2x+3y=2 and 3x-2y=1 .