Tardigrade
Tardigrade - CET NEET JEE Exam App
Exams
Login
Signup
Tardigrade
Question
Mathematics
The least value of 2x2 + y2 + 2xy + 2x - 3y + 8 for real numbers x and y is
Q. The least value of
2
x
2
+
y
2
+
2
x
y
+
2
x
−
3
y
+
8
for real numbers
x
and y is
1830
200
WBJEE
WBJEE 2015
Report Error
A
2
B
8
C
3
D
-1 /2
Solution:
2
x
2
+
y
2
+
2
x
y
+
2
x
−
3
y
+
8
=
2
1
[
4
x
2
+
2
y
2
+
4
x
y
+
4
x
−
6
y
+
16
]
=
2
1
[
(
y
2
−
8
y
)
+
(
4
x
2
+
y
2
+
4
x
y
+
4
x
+
2
y
)
+
16
]
=
2
1
[
(
y
−
4
)
2
+
(
2
x
+
y
+
1
)
2
−
1
]
So, least value will be
−
2
1
at
y
=
4
and
x
=
2
−
5
.