Processing math: 100%
Bridge, Algorithms, Math etc.
bridge hands and math and computer science and programming and puzzles and etc and etc.
Sunday, November 19, 2017
Surprising but easy
If
a
b
+
c
+
b
c
+
a
+
c
a
+
b
=
1
Show that
a
2
b
+
c
+
b
2
c
+
a
+
c
2
a
+
b
=
0
Solution
[Click here to expand/collapse]
Consider
a
+
b
+
c
=
(
a
+
b
+
c
)
(
a
b
+
c
+
b
c
+
a
+
c
a
+
b
)
This is the same as
a
+
b
+
c
+
a
2
b
+
c
+
b
2
c
+
a
+
c
2
a
+
b
And thus
a
2
b
+
c
+
b
2
c
+
a
+
c
2
a
+
b
=
0
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