Question

1. Daca x+y=4 si xy=3,atunci (x-y)^2=...?
2. x^2+y^2-6x -10+34=0,dacă x=...? si y=..?

Answer 1

1. xy=3⇒2xy=6
x+y=4 |()²
x²+2xy+y²=16
x²+y²+6=16
x²+y²=10 
...................
(x-y)²=x²-2xy+y²=10-6= 4

2.x²+y²-6x-10y+34=0
(x²-6x+9)+(y²-10y+25)=0
(x-3)²+(y-5)²=0
(x-3)²≥0
(y-5)²≥0
.................+
(x-3)²+(y-5)²≥0
Dar:(x-3)²+(y-5)²=0
Asadar; x-3=0⇒x=3
             y-5=0⇒y=5