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Daca x+y=4 si x patrat + y patrat=12, calculati x-y

Răspuns :

1) (x-y)^2 = x^2 - 2xy +y^2 = 12 - 2xy

(x+y)^2 = 16 = x^2+2xy+y^2

16=12+2xy

2xy=4 inlocuim in 1)

(x-y)^2 = 12-2xy = 12 - 4 = 8

(x-y)^2=8

lx-yl = 2√2 se ia diferenta in modul

daca x>y ⇒x-y=2√2

daca x<y⇒y-x = 2√2