If `x,y` are real numbers such that `xy< 1` then `Tan ^-1 x +Tan ^-1 y = Tan^-1 ( (x + y) / (1 - xy))`

If x,y,z are real numbers such that xy=6,x-z=2 and x+y+z=9, compute (x)/(y)-(z)/(x)-(z^(2))/(xy)

If x and y are real numbers such that sin^2theta=(x^2+y^2)/(2xy) show that x=y .

If x and y are real number such that x^(2)+2xy-y^(2)=6, find the minimum value of (x^(2)+y^(2))^(2)

x,y,z are real numbers such that x+y+z=3 and xy+yz+zx=a (where a is a real parameter). Determine the value of 'a' for which the difference between the maximum and minimum value of x is equal to 8.

Find all ordered pairs (x,y) of real numbers such that x^(2)+4y^(2)-xy=10,2x-4y+3xy=11

Find all ordered triples (x,y,z) of real numbers such that x-sqrt(yz)=42,y-sqrt(zx)=6,z-sqrt(xy)=-30

If x, y, z are positive real numbers such that x+y+z=a, then

For a real number r we denote by [r] the largest integer less than or equal to r. If x,y are real numbers with x,y>=1 then which of the following statements is always true? A) [x+y]<=[x]+[y]B)[xy]<=[x][y]c)[2^(x)]<=2^(x)D)[(x)/(y)]<=(x)/(y)

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

If x and y are positive real numbers such that x^3+8y^3+24xy=64 , then the value of 1/(x+2y) is