x + y = 5√11
x · y = 66 ⇒ x = 66/y
Inlocuim in suma:
66/y + y = 5√11 → le aduc la acelasi numitor comun(y)
66 + y² = 5√11y
y² - 5√11 y + 66 = 0 → ecuatie de gradul II
Δ = 25 ×11 - 4 ×66 = 275 - 264 = 11
Δ = 11
x₁ = ( 5√11 + √11) /2 = 6√11/2 = 3√11
x₂ = ( 5√11 - √11) /2 = 4√11/2 = 2√11
Verific: 3√11 + 2√11 = 5√11 → suma
3√11 × 2√11 = 6 × 11 = 66 → produsul
