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UPSC 2014 CDS II Math Paper
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© examsnet.com
Question : 34
Total: 100
If
a
x
+
b
y
−
2
=
0
and
a
x
b
y
=
1
, where a ≠ 0, b ≠ 0, then what is
(
a
2
x
+
b
2
y
)
equal to?
[2014 CDS-II]
a
+
b
2
a
b
a
3
+
b
3
a
2
+
b
2
Validate
Solution:
The given equations are
a
x
+
b
y
−
2
=
0
and axby = 1 (a, b≠ 0)
a
b
+
b
y
+
2
=
0
⇒
1
b
y
−
2
=
0
(
a
x
=
1
b
y
)
⇒
(
b
y
−
1
)
2
=
0
⇒
b
y
=
1
⇒
y
=
1
b
So,
a
x
=
1
⇒
x
=
1
a
∴
a
2
x
+
b
2
y
=
a
2
×
1
a
+
b
2
×
1
b
=
a
+
b
© examsnet.com
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