Question

se (x+y)²=400 e xy=100,determine o valor de x²+y²

Answer 1

(x + y)² = 400 = x + y = \|400 = x + y = 20

x + y = 20
xy = 100

y = 20 - x

x(20 - x) =100
-x² + 20x - 100 = 0 (-1)
x² - 20x + 100 = 0
a = 1, b = -20 e c=100
delta = b² - 4ac
d = (-20)² - 4 x 1 x 100
d = 400 - 400
d = 0

x = -b
     2a
x = 20
       2
x = 10

y = 20 - x
y = 20 - 10
y = 10

x² + y² =
10² + 10² =
100 + 100 = 200