Question

Aflati numerele reale x si y pentru care x^{2} + y^{2} + 45 = 6(x+2y)

Answer 1

(a+b)^2=a^2+2ab+b^2

x^2+y^2+45=6x+12y
x^2-6x+y^2-12y+45=

x^2-2*3x+3^2=x^2-6x+9=(x-3)^2
45-9=36

Deci x-ul e cam rezolvat
(x-3)^2+y^2-12y+36
y^2-12y+36=(y-6)^2

(x-3)^2+(y-6)^2=0
x-3=0=>x=3
y-6=0=>y=6