Sākums

LV.AMO.2005.10.1   lv

Vai noteikti \(x+\frac{9}{x}>y+\frac{9}{y}\), ja

(A) \(x>y>0\), (B) \(x>y>3\)?

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Atrisinājums

(A) nē; piemēram, \(x=1\) un \(y=0,00001\).

(B) jā, jo \(\left(x+\frac{9}{x}\right)-\left(y+\frac{9}{y}\right)=(x-y)\left(1-\frac{9}{xy}\right)>0\).