Question

Arătați că:
a) daca a <b, atunci
$\frac{1}{a} > \frac{1}{b}$
b) daca a >b, atunci
$\frac{1}{a} < \frac{1}{b}$
, a, b, €, N*

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Answer 1

a si b ∈N*

a<b    |:(a•b)

a/(a•b)<b/(a•b)

=> 1/b<1/a

sau, 1/a>1/b

a>b      |:(a•b)

a/(a•b)>b/(a•b)

=> 1/b>1/a

sau, 1/a<1/b