If (x+y)^2=78 and xy=13, what is (x-y)^2?

(x+y)^2=x^2+y^2+2xy=78

x^2+y^2+2(13)=78

x^2+y^2=52

(x-y)^2=x^2+y^2-2xy, 52-2(13)=52-26=26,

-tertre

( x + y)^2  = 78

x^2 + 2xy + y^2  = 78

If xy = 13 .....then

x^2 + y^2 + 2(13) = 78

x^2 + y^2 + 26 = 78

x^2 + y^2  = 52

So

(x - y)^2  =  

x^2 - 2xy + y^2  =

(x^2 + y^2) - 2xy =

(52) - 2(13)  =

26