Question

sabendo que x+y=3 e xy= 1 calcule :

Answer 1

X + Y = 3
X = 3-y
X*y = 1
Y(3-y) = 1
3Y - Y² = 1
-y² +3y - 1 = 0

$x' = \frac {-3 +\sqrt{5}}{-2}$
$x'' = \frac {-3 +\sqrt{5}}{-2}$

Answer 2

sistema linear:
x + y = 3
xy = 1------x = 1/y ou y = 1/x

substitui em x + y = 3, fica assim:
1/y + y = 3
mmc = y
1 + y" = 3y
y" - 3y + 1 = 0
delta = b" - 4.a.c
delta = (-3)" - 4.1.1
delta = 9 - 4
delta = 5

x = - b +_ raiz delta / 2.a
x = - (-3)+_ raiz 5 / 2
x = 3 +_ raiz 5 / 2

x* = 3 - raiz 5 / 2
x** = 3 + raiz 5 /2

agora para achar o valor de y:

y = 1/x
y = 1 / (3 - raiz 5 / 2)
y = 1 * 2/ 3 - raiz 5
y = 2 / 3 - raiz 5
y = 2/ 3 - raiz 5 * 3 + raiz 5 / 3 + raiz 5
y = 6 + raiz 5 / 9 - 5

6 + raiz 5
y = ------------
4