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2012 Centers of Excellency of Suceava
1
Easy algebraic identity
Easy algebraic identity
Source:
October 31, 2019
algebra
formula
Problem Statement
Let be three nonzero rational numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
under the relation
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
=
a
2
b
2
c
2
.
(a+b)(b+c)(c+a)=a^2b^2c^2.
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
=
a
2
b
2
c
2
.
Show that the expression
3
+
1
/
a
3
+
1
/
b
3
+
1
/
c
3
3
\sqrt[3]{3+1/a^3+1/b^3+1/c^3}
3
3
+
1/
a
3
+
1/
b
3
+
1/
c
3
is rational. Ion Bursuc
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