Question

x, y apartim (2, infintit) demonstrarti poza​

Answer 1

Răspuns:

(xy-2)/(x+y-4)>2

(xy-2)>2(x+y-4)

xy>2x+2y-8+2

xy-2x-2y>-6

(xy-2x)-2y> -6

x(y-2)-2y>-2-4

x(y-2)-2y+4>-2

x(y-2)-2(y-2)>-2

(y-2)(x-2)>-2

deoarece x, y∈(2,∞)=>

x-2>0 si y-2>0

=.>

(x-2)(y-2)>0>-2

QED

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