MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2016 Hanoi Open Mathematics Competitions
3
3
Part of
2016 Hanoi Open Mathematics Competitions
Problems
(1)
max of M=a^2+b^2- ab when a^3 +b^3 = a^5 +b^5 (HOMC 2016 J Q3)
Source:
8/6/2019
Given two positive numbers
a
,
b
a,b
a
,
b
such that
a
3
+
b
3
=
a
5
+
b
5
a^3 +b^3 = a^5 +b^5
a
3
+
b
3
=
a
5
+
b
5
, then the greatest value of
M
=
a
2
+
b
2
−
a
b
M = a^2 + b^2 - ab
M
=
a
2
+
b
2
−
ab
is(A):
1
4
\frac14
4
1
(B):
1
2
\frac12
2
1
(C):
2
2
2
(D):
1
1
1
(E): None of the above.
inequalities
maximum
algebra