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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
10.3
\sqrt{x(x+7)}+\sqrt{(x+7)(x+17)}+... (III Soros Olympiad 1996-97 R3 10.3)
\sqrt{x(x+7)}+\sqrt{(x+7)(x+17)}+... (III Soros Olympiad 1996-97 R3 10.3)
Source:
May 31, 2024
algebra
Radicals
Problem Statement
Solve the equation
x
(
x
+
7
)
+
(
x
+
7
)
(
x
+
17
)
+
(
x
+
17
)
(
x
+
24
)
=
12
+
17
2
\sqrt{x(x+7)}+\sqrt{(x+7)(x+17)}+\sqrt{(x+17)(x+24)}=12+17\sqrt2
x
(
x
+
7
)
+
(
x
+
7
)
(
x
+
17
)
+
(
x
+
17
)
(
x
+
24
)
=
12
+
17
2
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