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Moscow Mathematical Olympiad
1949 Moscow Mathematical Olympiad
161
MMO 161 Moscow MO 1949 x^2+2ax+1/16=-a+\sqrt{a^2 +x-1/16}
MMO 161 Moscow MO 1949 x^2+2ax+1/16=-a+\sqrt{a^2 +x-1/16}
Source:
July 20, 2019
radical
equation
algebra
parameter
Problem Statement
Find the real roots of the equation
x
2
+
2
a
x
+
1
16
=
−
a
+
a
2
+
x
−
1
16
x^2 + 2ax + \frac{1}{16} = -a +\sqrt{ a^2 + x - \frac{1}{16} }
x
2
+
2
a
x
+
16
1
=
−
a
+
a
2
+
x
−
16
1
,
(
0
<
a
<
1
4
)
\left(0 < a < \frac14 \right)
(
0
<
a
<
4
1
)
.
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