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Por dato:
a + b = 12 ............................... (I)
a.b = 9
Se tiene:
a^2 + b^2 + 2ab = (a + b)^2
Reemplazando:
a^2 + b^2 +2 (9) = (12)^2
a^2 + b^2 = 144 - 18
a^2 + b^2 = 126 ......................(II)
Asimismo:
a^2 + b^2 - 2ab = (a - b)^2
Reemplazando:
126 - 2(9) = (a - b)^2
108 = (a - b)^2
6√3 = a - b ...................... (II)
Sumando (I) y (III) se tiene:
a = 6 + 3√3
b = 6 - 3√3