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12
Determine the minimum value
Determine the minimum value
Source:
February 17, 2016
inequalities
Problem Statement
Suppose that
a
>
0
;
b
>
0
a > 0; b > 0
a
>
0
;
b
>
0
and
a
+
b
≤
1
a + b \leq 1
a
+
b
≤
1
. Determine the minimum value of
M
=
1
a
b
+
1
a
2
+
a
b
+
1
a
b
+
b
2
+
1
a
2
+
b
2
M=\frac{1}{ab} +\frac{1}{a^2+ab}+\frac{1}{ab+b^2}+\frac{1}{a^2+b^2}
M
=
ab
1
+
a
2
+
ab
1
+
ab
+
b
2
1
+
a
2
+
b
2
1
.
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