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Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
11.3
x - \sqrt{x^2-a^2} = (x-a)^2}/2(x+a) (V Soros Olympiad 1998-99 Round 2 11.3)
x - \sqrt{x^2-a^2} = (x-a)^2}/2(x+a) (V Soros Olympiad 1998-99 Round 2 11.3)
Source:
May 25, 2024
algebra
Problem Statement
For each value of parameter
a
a
a
, solve the the equation
x
−
x
2
−
a
2
=
(
x
−
a
)
2
2
(
x
+
a
)
x - \sqrt{x^2-a^2} = \frac{(x-a)^2}{2(x+a)}
x
−
x
2
−
a
2
=
2
(
x
+
a
)
(
x
−
a
)
2
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