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2000 Moldova National Olympiad
Problem 2
algebraic identity (Moldova MO 2000 Grade 7 P2)
algebraic identity (Moldova MO 2000 Grade 7 P2)
Source:
April 23, 2021
algebra
Problem Statement
Prove that if real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
satisfy
a
2
+
b
2
+
(
a
+
b
)
2
=
c
2
+
d
2
+
(
c
+
d
)
2
a^2+b^2+(a+b)^2=c^2+d^2+(c+d)^2
a
2
+
b
2
+
(
a
+
b
)
2
=
c
2
+
d
2
+
(
c
+
d
)
2
, then they also satisfy
a
4
+
b
4
+
(
a
+
b
)
4
=
c
4
+
d
4
+
(
c
+
d
)
4
a^4+b^4+(a+b)^4=c^4+d^4+(c+d)^4
a
4
+
b
4
+
(
a
+
b
)
4
=
c
4
+
d
4
+
(
c
+
d
)
4
.
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