I f`(x+a)^2+(y+b)^2=4(a x+b y),` where `x,a,y,b` are real, the value of `xy-ab` is :

Let x,y,z are positive real numbers satisfying x+y+z=1 . If the maximum value of x^(3)y^(2)z can be expressed as (a)/(b) where a and b are co-prime,then the value of (a+b) is

If 4x^(2) + y^(2)=a and xy= b , find the value of 2x+y

If a=xy^(2) and b=x^(3)y^(5) where x and y are prime numbers then LCm of (a,b) is _____________.

If xy=a^2 and S = b^2x + c^2y where a, b and c are constants then the minimum value of S is

If f(2x + 3y, 2x-3y)=4xy , then find the value of f(x,y)

Consider y=(2x)/(1+x^(2)), where x is real,then the range of expression y^(2)+y-2 is [a,b]* find b-4a.

If f(x)f(y) = f(x) + f(y) + f(xy) -2 for all real values of x and y and f(2) = 5, find f(4) and f(1/4) .