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.`

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

If x,y in R^(+) such that x + y = 8, then find the minimum value of (1 + (1)/(x)) (1 + (1)/(y))

If x , y in R satisfies (x+5)^2+(y-12)^2=(14)^2, then the minimum value of sqrt(x^2+y^2) is__________

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

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

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

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.

If R={(x,y): x,y in W, x ^(2)+y^(2)=25} , then find the domain and range or R.