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Byju's Answer
Standard IX
Mathematics
Exponential Representation for Irrational Numbers
If x a + y ...
Question
If
x
a
+
y
b
=
1
and
x
2
a
2
+
y
2
b
2
=
a
b
a
+
b
then prove that
x
n
+
1
a
+
y
n
+
1
b
=
(
a
b
a
+
b
)
n
.
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Solution
Solving the first two equations for
x
and
y
we have by eliminating
y
,
[
(
a
+
b
)
x
−
a
b
]
2
=
0
∴
x
=
a
b
a
+
b
=
y
.
x
n
+
1
a
+
y
n
+
1
b
=
(
a
b
a
+
b
)
n
+
1
[
1
a
+
1
b
]
=
(
a
b
a
+
b
)
n
+
1
[
a
+
b
a
b
]
=
(
a
b
a
+
b
)
n
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