Question

Wykaż, że jeśli x^{2}+y^{2}=3 i x-y=-2 to xy = 1/2

daje naj

poziom 1 liceum

Answer 1

 

(-2)^{2}=(x-y)^{2}= x^{2} + y^{2} -2xy = 3-2xy

 

=> 4=3-2xy

=> 2xy= (3-4)

=> xy =-1/2

 

Answer 2

x² + y² = 3

x + y = - 2

 

 

x² + y² = (x + y)² - 2xy

3 = (-2)² - 2xy

3 = 4 - 2xy

3 - 4 = - 2xy

-1 = -2xy

1-/(-2) = xy

xy = 1/2       --------------  odpowiedź