the two number are x and y
x + 2y = 11
x * y = 12
[tex]\left \{ {{x + 2y = 11} \atop {x * y = 12}} \right.[/tex]
[tex]\left \{ {{x = 11 - 2y} \atop {x * y = 12}} \right.[/tex]
so, using the sostituzion metod
[tex]\left \{ {{x = 11 - 2y} \atop {(11-2y) * y = 12}} \right.[/tex]
[tex]\left \{ {{x = 11 - 2y} \atop {(11y - 2y² = 12}} \right.[/tex]
[tex]\left \{ {{x = 11 - 2y} \atop {(11y - 2y² - 12 = 0}} \right.[/tex]
................................................
11y - 2y² - 12 = 0
2y² - 11y + 12 = 0
Δ = 121 - 96 = 25
y1,2 = (11 ± 5)/4
y1 = (11 - 5)/4 = 6/4 = 3/2
y2 = (11 + 5)/4 = 16/4 = 4
x+2y = x + 2 * 3/2 = 11
x = 8
x+2y = x + 2 * 4 = 11
x = 3 not accetable because x must be larger than y
the couple of numbers 8 and 3/2 (8+2*3/2=11) and (8*3/2=12)
