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Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Factorization Method
Solve the fol...
Question
Solve the following equation:
12
x
2
+
1
x
2
-
56
x
+
1
x
+
89
=
0
Open in App
Solution
We
have
12
x
2
+
1
x
2
-
56
x
+
1
x
+
89
=
0
We
know
the
identity
x
2
+
1
x
2
=
x
+
1
x
2
-
2
Thus
,
the equation can be written as
:
12
x
+
1
x
2
-
2
-
56
x
+
1
x
+
89
=
0
12
x
+
1
x
2
-
24
-
56
x
+
1
x
+
89
=
0
12
x
+
1
x
2
-
56
x
+
1
x
+
65
=
0
L
e
t
m
=
x
+
1
x
.
Then, the equation can be further written as:
12
m
2
-
56
m
+
65
=
0
On
using
the
quadratic
formula
,
we
get
:
m
=
-
-
56
±
-
56
2
-
4
12
65
2
12
=
56
±
3136
-
3120
24
=
56
±
16
24
=
56
±
4
24
=
60
24
,
52
24
=
5
2
,
13
6
On
substituting
m
=
x
+
1
x
,
we
get
:
x
+
1
x
=
5
2
.
.
.
.
(
1
)
o
r
x
+
1
x
=
13
6
.
.
.
(
2
)
Now
from
equation
(
1
)
,
we
get
:
x
+
1
x
=
5
2
⇒
x
2
+
1
x
=
5
2
⇒
2
x
2
+
2
=
5
x
⇒
2
x
2
-
5
x
+
2
=
0
On
splitting
the
middle
term
-
5
x
as
-
x
-
4
x
,
we
get
:
2
x
2
-
x
-
4
x
+
2
=
0
⇒
x
2
x
-
1
-
2
2
x
-
1
=
0
⇒
2
x
-
1
x
-
2
=
0
⇒
2
x
-
1
=
0
or
x
-
2
=
0
⇒
x
=
1
2
or
x
=
2
Now
,
from
equation
(
2
)
,
we
get
:
x
+
1
x
=
13
6
⇒
x
2
+
1
x
=
13
6
⇒
6
x
2
+
6
=
13
x
⇒
6
x
2
-
13
x
+
6
=
0
On
splitting
the
middle
term
-
13
x
as
-
9
x
-
4
x
,
we
get
:
6
x
2
-
9
x
-
4
x
+
6
=
0
⇒
3
x
2
x
-
3
-
2
2
x
-
3
=
0
⇒
2
x
-
3
3
x
-
2
=
0
⇒
2
x
-
3
=
0
or
3
x
-
2
=
0
⇒
x
=
3
2
or
x
=
2
3
Thus
,
the
solutions
of
the
given
equation
are
x
=
1
2
,
2
,
2
3
,
3
2
.
Suggest Corrections
1
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