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1
Find the value of the expression in fractions[Slovenia 2010]
Find the value of the expression in fractions[Slovenia 2010]
Source:
November 14, 2010
algebra proposed
algebra
Problem Statement
Let
a
,
b
a,b
a
,
b
be real numbers such that
∣
a
∣
≠
∣
b
∣
|a| \neq |b|
∣
a
∣
=
∣
b
∣
and
a
+
b
a
−
b
+
a
−
b
a
+
b
=
6.
\frac{a+b}{a-b}+\frac{a-b}{a+b}=6.
a
−
b
a
+
b
+
a
+
b
a
−
b
=
6.
Find the value of the expression
a
3
+
b
3
a
3
−
b
3
+
a
3
−
b
3
a
3
+
b
3
.
\frac{a^3+b^3}{a^3-b^3}+\frac{a^3-b^3}{a^3+b^3}.
a
3
−
b
3
a
3
+
b
3
+
a
3
+
b
3
a
3
−
b
3
.
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