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Byju's Answer
Standard XIII
Mathematics
Method of Intervals
If √9x2+6x+1<...
Question
If
√
9
x
2
+
6
x
+
1
<
2
−
x
,
then integral values of
x
is/are
A
−
2
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B
0
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C
−
1
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D
1
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Solution
The correct option is
C
−
1
Given
√
9
x
2
+
6
x
+
1
<
2
−
x
will be true
if
9
x
2
+
6
x
+
1
≥
0
⇒
(
3
x
+
1
)
2
≥
0
,
∀
x
∈
R
Now as
√
9
x
2
+
6
x
+
1
>
0
squaring both sides
⇒
9
x
2
+
6
x
+
1
<
(
2
−
x
)
2
⇒
9
x
2
+
6
x
+
1
<
4
+
x
2
−
4
x
⇒
8
x
2
+
10
x
−
3
<
0
⇒
(
2
x
+
3
)
(
4
x
−
1
)
<
0
∴
x
∈
(
−
3
2
,
1
4
)
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0
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