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Byju's Answer
Standard XI
Mathematics
Properties of Iota
x 2+ y 2+ xy ...
Question
x
2
+
y
2
+
x
y
=
1
for all
x
,
y
∈
R
,
the minimum value of
x
3
y
+
x
y
3
+
4
is
(correct answer + 1, wrong answer - 0.25)
A
1
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B
3
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C
4
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D
2
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Solution
The correct option is
D
2
Let
x
y
=
t
x
2
+
y
2
+
x
y
=
1
⇒
x
2
+
y
2
=
1
−
t
≥
0
⇒
t
≤
1
∀
t
∈
R
x
2
+
y
2
+
x
y
=
1
⇒
(
x
+
y
)
2
=
1
+
t
≥
0
⇒
t
≥
−
1
∀
t
∈
R
⇒
−
1
≤
t
≤
1
f
(
t
)
=
t
(
x
2
+
y
2
)
+
4
=
t
(
1
−
t
)
+
4
=
t
−
t
2
+
4
=
−
[
t
2
−
t
−
4
]
f
(
t
)
=
−
[
(
t
−
1
2
)
2
−
17
4
]
=
17
4
−
(
t
−
1
2
)
2
∴
f
(
t
)
min
=
17
4
−
(
−
1
−
1
2
)
2
=
2
which is occur when
t
=
x
y
=
−
1
Suggest Corrections
0
Similar questions
Q.
x
2
+
y
2
+
x
y
=
1
for all
x
,
y
∈
R
,
the minimum value of
x
3
y
+
x
y
3
+
4
is
(correct answer + 1, wrong answer - 0.25)
Q.
If
f
(
x
)
is a polynomial of degree
4
such that
lim
x
→
−
1
f
(
x
)
(
x
+
1
)
3
=
1
and
f
′′′
(
0
)
=
−
12
, then the maximum value of
f
(
x
)
is
(correct answer + 1, wrong answer - 0.25)
Q.
The minimum value of
sec
4
θ
1
tan
2
θ
2
+
sec
4
θ
2
tan
2
θ
1
, wherever defined, is
(correct answer + 1, wrong answer - 0.25)
Q.
If
x
1
+
x
2
+
x
3
=
0
,
y
1
+
y
2
+
y
3
=
0
and
x
1
y
1
+
x
2
y
2
+
x
3
y
3
=
0
,
then the value of
x
2
1
x
2
1
+
x
2
2
+
x
2
3
+
y
2
1
y
2
1
+
y
2
2
+
y
2
3
is
(correct answer + 2, wrong answer - 0.50)
Q.
If
f
(
x
)
=
30
−
2
x
−
x
3
, then the number of positive integral value(s) of
x
satisfying
f
(
f
(
f
(
x
)
)
)
>
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(
−
x
)
)
is
(correct answer + 1, wrong answer - 0.25)
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