Question

sabendo que x+y= 14 e x² + y²=116, calcule o valor de xy e de (x-y)²

Answer 1

x + y = 14 >>>> x = 14 - y  ****
x² + y² = 116

( 14 - y)²  + y² = 116
( 196 - 28y + y² ) + y² = 116
2y² - 28y + 196 - 116 = 0
2y² - 28y  + 80= 0
y² - 14y + 40 = 0
delta  = 196 - 160 = 36 ou +-V36 = +-6 ***
y = ( 14 +- 6)/2
y1 = 20/2 = 10
y2 = 8/2 = 4 ***

x1 = 14 - 10 = 4 ***
x2 = 14 - 4 = 10 ***
x = 4***
y = 10 ***

xy = 4 * 10  = 40 ****
( x - y)² = (4 - 10)² = ( -6)²  = 36 ***