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1988 Greece Junior Math Olympiad
4
algebraic exrpessions - Greece Juniors 1988 p4
algebraic exrpessions - Greece Juniors 1988 p4
Source:
September 13, 2024
algebra
Problem Statement
i) If
b
2
+
c
2
=
a
2
,
b
≠
±
c
b^2+c^2=a^2, \,\,\,\, b\ne \pm c
b
2
+
c
2
=
a
2
,
b
=
±
c
, calculate the expression
b
3
+
c
3
b
+
c
+
b
3
−
c
3
b
−
c
\frac{b^3+c^3}{b+c}+\frac{b^3-c^3}{b-c}
b
+
c
b
3
+
c
3
+
b
−
c
b
3
−
c
3
.ii) If
a
+
1
a
=
k
,
a
≠
0
a+\frac{1}{a}=k, a\ne 0
a
+
a
1
=
k
,
a
=
0
, find the expression
a
4
+
1
a
4
a^4+\frac{1}{a^4}
a
4
+
a
4
1
in terms of
k
k
k
.
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