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UPSC CDS Math Basic operation and Factorisation Questions
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© examsnet.com
Question : 11
Total: 77
If
1
+
p
x
1
−
p
x
√
1
−
q
x
1
+
q
x
= 1, then what are the non-zero solutions of x ?
[2019 CDS-I]
±
1
p
√
2
p
−
q
q
, 2 p ≠ q
±
1
p
q
√
p
−
q
, p ≠ q
±
p
q
√
p
−
q
, p ≠ q
±
q
p
√
2
p
−
q
, 2p ≠ q
Validate
Solution:
1
+
p
x
1
−
p
x
√
1
−
q
x
1
+
q
x
=
1
⇒
1
+
p
x
1
−
p
x
=
√
1
+
q
x
1
−
q
x
⇒
(
1
+
p
x
1
−
p
x
)
2
=
1
+
q
x
1
−
q
x
⇒
(
1
+
p
2
x
2
+
2
p
x
)
(
1
−
q
x
)
=
(
1
+
p
2
x
2
−
2
p
x
)
(
1
+
q
x
)
⇒
1
+
p
2
x
2
+
2
p
x
−
q
x
−
p
2
q
x
3
−
2
p
q
x
2
=
1
+
p
2
x
2
−
2
p
x
+
q
x
+
p
2
q
x
3
−
2
p
q
x
2
⇒
2
p
x
−
q
x
−
p
2
q
x
3
=
−
2
p
x
+
q
x
+
p
2
q
x
3
⇒
−
4
p
x
+
2
q
x
+
2
p
2
q
x
3
=
0
⇒
−
2
p
+
q
+
p
2
q
x
2
=
0
⇒
x
2
=
2
p
−
q
p
2
q
⇒
x
=
±
1
p
√
2
p
−
q
q
Hence
2
p
≠
q
© examsnet.com
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