Show that among all positive numbers `x` and `y` with `x^2+y^2=r^2,` the sum `x+y` is largest when `x=y=r/(sqrt(2))` .

Show that among all positive numbers x and y with x^(2)+y^(2)=r^(2), the sum x+y is larger when x=y=r/sqrt(2)

If R_2={(x,y)| x and y are integers and x^2 +y^2=64 } is a relation. Then find R_2 .

Show that the relation R on the set of natural numbers defined as R:{(x,y):y-x is a multiple of 2} is an equivalance relation

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If x=2sqrt(5)+sqrt(3) and y=2sqrt(5)-sqrt(3) , then x^(4)+y^(4) =

Let P={(x,y)//x in R, y in R, x^(2)+y^(2)=1} , then P is

For real numbers x and y define x\ R\ y if x - y + sqrt(2) is an irrational number. Then the relation R is

Show that the function ,y, defined by y(x) = sqrt(1+x^(2)) (x in R) is the solution of (1+x^(2))y' = xy

If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5) then

If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5) then

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