If `x^2+y^2=4` then find the maximum value of `(x^3+y^3)/(x+y)`

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

Let x,y in R , then find the maximum and minimum values of expression (x^(2)+y^(2))/(x^(2)+xy+4y^(2)) .

For any x,y, in R,xygt0 . Then the minimum value of (2x)/(y^3)+(x^3y)/(3)+(4y^2)/(9x^4) is ___________.

If (x,y) lies on the ellipse x^(2)+2y^(3) = 2 , then maximum value of x^(2)+y^(2)+ sqrt(2)xy - 1 is

If x,y,in R^(+) satisfying x+y=3 , then the maximum value of x^2y is _____________.

If (x+1, y-2)=(3,1), find the values of x and y.

If (x_i ,y_i),i=1,2,3, are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2, then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3) .