Question

Calculati x si y
5x^2+3y^2+10radical din 5x+6radical din 3y+34=0

Answer 1

5x² + 3y² + 10√5x + 6√3y + 34 = 0
5x² +2·5·√5x + 25 + 3y² + 2·3·√3x + 9 = 0
5·(x² + 2·√5x + 5) +3·(y² +2·√3x + 3) = 0
5·(x+√5)² + 3·(y+√3)² = 0
        ↓                 ↓
≥0,∀ x ∈ R      ≥0,∀ y ∈ R

                    ↓↓
5·(x+√5)² = 0 → (x+√5)² = 0 → x+√5 = 0 → x = - √5
3·(y+√3)² = 0 → (y+√3)² = 0 → y+√3 = 0 → y = -√3

  ⇒ (x,y) ∈ { (-√5,-√3) }