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Spain Mathematical Olympiad
1990 Spain Mathematical Olympiad
1
1
Part of
1990 Spain Mathematical Olympiad
Problems
(1)
compare \sqrt{3}+\sqrt{10+2\sqrt{3}} with \sqrt{5+\sqrt{22}}+\sqrt{8-\sqrt{22}}}
Source: Spanish Mathematical Olympiad 1990 P1
8/2/2018
Prove that
x
+
y
+
x
y
\sqrt{x}+\sqrt{y}+\sqrt{xy}
x
+
y
+
x
y
is equal to
x
+
y
+
x
y
+
2
y
x
\sqrt{x}+\sqrt{y+xy+2y\sqrt{x}}
x
+
y
+
x
y
+
2
y
x
and compare the numbers
3
+
10
+
2
3
\sqrt{3}+\sqrt{10+2\sqrt{3}}
3
+
10
+
2
3
and
5
+
22
+
8
−
22
+
2
15
−
3
22
\sqrt{5+\sqrt{22}}+\sqrt{8- \sqrt{22}+2\sqrt{15-3\sqrt{22}}}
5
+
22
+
8
−
22
+
2
15
−
3
22
.
algebra
radical