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TOT 3981993 Autumn A S6 x^4+ax^3+2x^2+bx+1=0
TOT 3981993 Autumn A S6 x^4+ax^3+2x^2+bx+1=0
Source:
June 12, 2024
algebra
inequalities
polynomial
Problem Statement
If it is known that the equation
x
4
+
a
x
3
+
2
x
2
+
b
x
+
1
=
0
x^4+ax^3+2x^2+bx+1=0
x
4
+
a
x
3
+
2
x
2
+
b
x
+
1
=
0
has a (real) root, prove the inequality
a
2
+
b
2
≥
8.
a^2+b^2 \ge 8.
a
2
+
b
2
≥
8.
(A Egorov)
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