Question

Resolva os Sistemas:
a) X+Y=1
9XY=2

b) X-Y=3
X²-Y²=15

Responda explicando passo a passo, Por Favor

Answer 1

A) x+y=1
9xy=2

x=1-y
9.(1-y).y=2
(9-9y)y=2
9y-9y²-2 = 0
a = -9; b = 9; c = -2
Δ = b²-4.a.c
Δ = 81 - 72
Δ = 9

x = -b+-√Δ / 2a
x = -9+-3 / -18
x = -12/-18
x = -2/-3 = +2/3
x' = -9+3 / -18
x' = -6/-18
x' = -1/-3 = +1/3

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B)
x-y=3
x²-y²=15
x = 3+y
(3+y)² -y² = 15
(3+y)(3+y) - y² = 15
9+3y+3y+y² - y² = 15
9+6y = 15
6y = 15-9
6y = 6
y = 1

Voltando...
x-y=3
x-1=3
x=3+1
x = 4