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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2004 Junior Balkan Team Selection Tests - Moldova
8
8
Part of
2004 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
ab in terms of inverse and sum / differences of a,b
Source: 2004 Moldova JBMO TST p8
2/20/2021
The positive real numbers
a
a
a
and
b
b
b
(
a
>
b
a> b
a
>
b
) are written on the board. At every step, with numbers written on the board, one of the following operations can be performed: a) choose one of the numbers and write its square or its inverse. b) choose two numbers written on the board ¸and write their sum or their positive difference. Show how the product
a
⋅
b
a \cdot b
a
⋅
b
can be obtained with the help of the defined operations.
algebra
Product