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KVPY SX SB Exam 2012 Question Paper
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© examsnet.com
Question : 2
Total: 120
In the real number system, the equation
√
x
+
3
−
4
√
x
−
1
+
√
x
+
8
−
6
√
x
−
1
=
1
has
no solution
exactly two distinct solutions
exactly four distinct solutions
infinitely many solutions
Validate
Solution:
√
x
+
3
−
4
√
x
−
1
+
√
x
+
8
−
6
√
x
−
1
=
1
;
x
≥
1
√
(
x
−
1
)
−
2
×
2
√
x
−
1
+
4
+
√
(
x
−
1
)
−
6
√
x
−
1
+
9
=
1
|
√
x
−
1
−
2
|
+
|
√
x
−
1
−
3
|
=
1
Case - I
√
x
−
1
−
2
+
√
x
−
1
−
3
=
1
(x ≥ 10)
2
√
x
−
1
=
6
x
=
10
Case -II
√
x
−
1
−
2
−
√
x
−
1
+
3
=
1
(5 ≤ x ≤ 10)
Case -III
−
√
x
−
1
−
2
−
√
x
−
1
+
3
=
1
(1 ≤ x ≤ 5)
2
√
x
−
1
=
4
x
=
5
© examsnet.com
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