x+y = 21
x²+y² = 223 ⇒ (x+y)²-2xy = 223
⇒ 21²-2xy = 223 = 441-2xy = 223
⇒ 2xy = 218 ⇒ xy = 109
x+y = 21
xy = 109
t² - St + P = 0
t² - 21t + 109 = 0
∆ = 21² - 4•109 = 441 - 436 = 5
⇒ t₁,₂ = (21±√5)/2
[tex]\Rightarrow (a,b) = \left\{\left(\dfrac{21-\sqrt 5}{2},\dfrac{21+\sqrt 5}{2}\right);\left(\dfrac{21+\sqrt 5}{2},\dfrac{21-\sqrt 5}{2}\right)\right\}[/tex]
