Question

If x and y are real numbers and x^2 + y^2 = 1, then the maximum value of (x + y)^2 is

Answer 1

(x+y)^2=(x^2+y^2)+2*x*y=1+2*x*y
To have maximum value of , x and y must be closest value eachother , x and y real numbers so you can say x=y ,
x^2+x^2=1 , 2*x^2=1 , x=y=1/root2
1+2*(1/root2)^2 =2