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min T=42a^2+34b^2+43c^2 when 18ab+9ca+29bc=1 (HOMC 2016 S Q15)
min T=42a^2+34b^2+43c^2 when 18ab+9ca+29bc=1 (HOMC 2016 S Q15)
Source:
September 8, 2019
inequalities
algebra
minimum
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be real numbers satisfying the condition
18
a
b
+
9
c
a
+
29
b
c
=
1
18ab + 9ca + 29bc = 1
18
ab
+
9
c
a
+
29
b
c
=
1
. Find the minimum value of the expression
T
=
42
a
2
+
34
b
2
+
43
c
2
T = 42a^2 + 34b^2 + 43c^2
T
=
42
a
2
+
34
b
2
+
43
c
2
.
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