X2 - 2016x= y2 - 2016y

Question

X2 - 2016x= y2 - 2016y

Comments

(x-y)(x+y -2016) =0 ⇔ [ y =x ; y = -x +2016 .

Answer 1

x²-2016*x=y²-2016*y

x²-y²-2016*x+2016*y=0

(x-y)*(x+y)-2016*(x-y)=0

(x-y)*(x+y-2016)=0

x=y

x+y-2016=0    x+y=2016       2x=2016  |÷2     x=1008     ⇒

Ответ: x=y=1008.