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CAT 2020 Exam Shift 1 Solved Paper
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© examsnet.com
Question : 59
Total: 76
How many distinct positive integer-valued solutions exist to the equation
(
x
2
−
7
x
+
11
)
(
x
2
−
13
x
+
42
)
=
1
?
6
8
2
4
Validate
Solution:
(
x
2
−
7
x
+
11
)
(
x
2
−
13
x
+
42
)
=
1
We know if
a
b
=
1
⇒
a
=
1
and
b
is any number
or
a
=
−
1
and
b
is even
a
>
0
and
b
is 0
case
1
:
x
2
−
13
x
+
42
=
0
⇒
x
=
6
,
7
case
2
:
x
2
−
7
x
+
11
=
1
⇒
x
2
−
7
x
+
10
=
0
⇒
x
=
2
or 5
case
3
:
x
2
−
7
x
+
11
=
−
1
⇒
x
2
−
7
x
+
12
=
0
⇒
x
=
4
or 3
Hence number of solutions are 6
© examsnet.com
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