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Kürschák Math Competition
1975 Kurschak Competition
1
1
Part of
1975 Kurschak Competition
Problems
(1)
ab^2 (1/(a + c)^2 +1/(a- c)^2 ) = (a -b)
Source: 1975 Hungary - Kürschák Competition p1
10/15/2022
Transform the equation
a
b
2
(
1
(
a
+
c
)
2
+
1
(
a
−
c
)
2
)
=
(
a
−
b
)
ab^2 \left(\frac{1}{(a + c)^2} +\frac{1}{(a- c)^2} \right) = (a -b)
a
b
2
(
(
a
+
c
)
2
1
+
(
a
−
c
)
2
1
)
=
(
a
−
b
)
into a simpler form, given that
a
>
c
≥
0
a > c \ge 0
a
>
c
≥
0
,
b
>
0
b > 0
b
>
0
.
algebra