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1979 Vietnam National Olympiad
1
triangle with sides x^4+ x^3+ 2x^2+ x+ 1, 2x^3+ x^2+ 2x+ 1, x^4 - 1 if x>1
triangle with sides x^4+ x^3+ 2x^2+ x+ 1, 2x^3+ x^2+ 2x+ 1, x^4 - 1 if x>1
Source: Vietnam MO 1979 P1
July 28, 2018
algebra
inequalities
Problem Statement
Show that for all
x
>
1
x > 1
x
>
1
there is a triangle with sides,
x
4
+
x
3
+
2
x
2
+
x
+
1
,
2
x
3
+
x
2
+
2
x
+
1
,
x
4
ā
1.
x^4 + x^3 + 2x^2 + x + 1, 2x^3 + x^2 + 2x + 1, x^4 - 1.
x
4
+
x
3
+
2
x
2
+
x
+
1
,
2
x
3
+
x
2
+
2
x
+
1
,
x
4
ā
1.
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