Question

Wykaż, że jeśli x²+y²=2 i x+y=1 to xy= - ½

Answer 1

 

Z: x² + y² = 2 ∧ x + y = 1

T:  xy = -0,5

D:

 

x² + y² = 2

(x+y)² = x² + 2xy + y²

(x+y)² - 2xy = 2

1² - 2xy = 2

-2xy = -1

xy = -0,5

 

 

 

 

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Litterarum radices amarae sunt, fructus iucundiores

 

Pozdrawiam :)

Answer 2

Jeżeli x²+y²=2 i x+y=1, to

(x+y)²-2xy=2, ponieważ   x+y=1, więc

1-2xy=2

-2xy=2-1

-2xy=1/:-2

xy=-1/2 c.n.d.