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Question
Mathematics
If x, y ∈ R then the minimum value of the expression E=x2+6 y2-2 x y+6 x-16 y+18 is
Q. If
x
,
y
∈
R
then the minimum value of the expression
E
=
x
2
+
6
y
2
−
2
x
y
+
6
x
−
16
y
+
18
is
230
115
Complex Numbers and Quadratic Equations
Report Error
A
3
B
4
C
5
D
6
Solution:
E
=
x
2
+
6
y
2
−
2
x
y
+
6
x
−
16
y
+
18
⇒
(
x
2
+
y
2
−
2
x
y
+
6
x
−
6
y
+
9
)
+
(
5
y
2
−
10
y
+
5
)
+
4
⇒
(
x
−
y
+
3
)
2
+
5
(
y
−
1
)
2
+
4
Min. value for
y
=
1
;
x
=
−
2
;
min
. value is 4 .