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Standard VIII
Mathematics
Question
If
x
a
2
x
b
2
=
x
16
,
x
>
1
,
and
a
+
b
=
2
, what is the value of
a
−
b
?
8
14
16
18
A
18
B
8
C
14
D
16
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Solution
Verified by Toppr
Given,
x
a
2
x
b
2
=
x
16
Also given,
x
>
1
and
a
+
b
=
2
..(1)
⇒
x
a
2
−
b
2
=
x
16
⇒
a
2
−
b
2
=
16
...(2) (When the non-zero base is the same, the index also must be the same)
Dividing equations (1) and (2),
∴
a
2
−
b
2
a
+
b
=
a
−
b
=
16
2
=
8
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