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Poland - Second Round
1954 Poland - Second Round
4
4
Part of
1954 Poland - Second Round
Problems
(1)
\sqrt{x - a} + \sqrt{x - b} = \sqrt{x - c }
Source: Polish MO second round 1954 p4
8/29/2024
Give the conditions under which the equation
x
−
a
+
x
−
b
=
x
−
c
\sqrt{x - a} + \sqrt{x - b} = \sqrt{x - c }
x
−
a
+
x
−
b
=
x
−
c
has roots, assuming that the numbers
a
a
a
,
b
b
b
,
c
c
c
are pairs of differences
algebra