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Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1976 Swedish Mathematical Competition
3
3
Part of
1976 Swedish Mathematical Competition
Problems
(1)
1/(b-c)^2 +1/(c-a)^2 +1/(a-b)^2 is square of a rational for rational a,b,c
Source: 1976 Swedish Mathematical Competition p3
3/26/2021
If
a
a
a
,
b
b
b
,
c
c
c
are rational, show that
1
(
b
−
c
)
2
+
1
(
c
−
a
)
2
+
1
(
a
−
b
)
2
\frac{1}{(b-c)^2}+\frac{1}{(c-a)^2}+\frac{1}{(a-b)^2}
(
b
−
c
)
2
1
+
(
c
−
a
)
2
1
+
(
a
−
b
)
2
1
is the square of a rational.
algebra
Perfect Square
rational