Sākums
Vai noteikti \(x+\frac{9}{x}>y+\frac{9}{y}\), ja
(A) \(x>y>0\), (B) \(x>y>3\)?
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(A) nē; piemēram, \(x=1\) un \(y=0,00001\).
(B) jā, jo \(\left(x+\frac{9}{x}\right)-\left(y+\frac{9}{y}\right)=(x-y)\left(1-\frac{9}{xy}\right)>0\).