Question

Sendo XY = 48 e x +2y =20 calcule o valor de
A) x²y+2y² b) (x+2y)² c) (x-2y)²

Answer 1

Bom dia 

xy = 48
x + 2y = 20 

x = 20 - 2y

(20 - 2y)*y = 48

20y - 2y² = 48

2y² - 20y + 48 = 0

y² - 10y + 24 = 0

delta
d² = 100 - 96 = 4
d = 2

y1 = (10 + 2)/2 = 12/2 = 6 , x1 = 20 - 2y1 = 20 - 12 = 8 
y2 = (10 - 2)/2 = 8/2 = 4 , x2 = 20 - 2y2 = 20 - 8 = 12 

x = 8, y = 6

a) x²y + 2y² = 8²*6 + 2*6² = 64*6 + 2*36 = 384 + 72 = 456
b) (x + 2y)² = (8 + 2*6)² = 20² = 400
c) (x - 2y)² = (8 - 2*6)² = (-4)² = 16 

x = 12, y = 4

a) x²y + 2y² = 12²*4 + 2*4² = 144*4 + 2*16 = 576 + 32 = 608
b) (x + 2y)² = (12 + 2*4)² = 20² = 400
c) (x - 2y)² = (12 - 2*4)² = 4² = 16