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Standard IX
Mathematics
Question
If
a
b
+
b
a
= 1, then
a
3
+
b
3
=
?
−
1
1
1
2
0
A
1
B
1
2
C
−
1
D
0
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Solution
Verified by Toppr
Given,
a
b
+
b
a
=
1
.
On simplifying,
a
b
+
b
a
=
1
⟹
a
2
+
b
2
a
b
=
1
⟹
a
2
+
b
2
=
a
b
⟹
a
2
+
b
2
−
a
b
=
0
−
−
(
i
)
.
We know,
a
3
+
b
3
=
(
a
+
b
)
(
a
2
+
b
2
−
a
b
)
.
Substitute
(
i
)
, we get,
a
3
+
b
3
=
(
a
+
b
)
(
0
)
⟹
a
3
+
b
3
=
0
.
Hence, option
D
is correct.
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2
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