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Section:
Mathematics
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© examsnet.com
Question : 1 of 11
Marks:
+1
,
-0
The sum of squares of all real solution of the equation
log
(
x
+
1
)
(
2
x
2
+
5
x
+
3
)
=
4
−
log
(
2
x
+
3
)
(
x
2
+
2
x
+
1
)
is equal to ______ .
[JEE Main 8 apr 2026 shift 2]
Your Answer:
Validate
Solution:
log
(
x
+
1
)
(
2
x
+
3
)
(
x
+
1
)
+
log
(
2
x
+
3
)
(
x
+
1
)
2
=
4
1
+
log
(
x
+
1
)
(
2
x
+
3
)
+
2
log
(
2
x
+
3
)
(
x
+
1
)
=
4
log
x
+
1
(
2
x
+
3
)
=
t
t
+
2
t
=
3
t
2
−
3
t
+
2
=
0
⇒
t
=
1
,
2
for
t
=
1
⇒
log
(
x
+
1
)
(
2
x
+
3
)
=
1
⇒
2
x
+
3
=
x
+
1
⇒
x
=
−
2
(
r
e
j
e
c
t
e
d
)
for
t
=
2
⇒
2
x
+
3
=
x
2
+
2
x
+
1
⇒
x
2
=
2
⇒
x
=
±
√
2
rejecting
x
=
−
√
2
, we get
x
=
√
2
∴ sum of squares of all the roots = 2
© examsnet.com
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