1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard VIII
Mathematics
Factorisation Using Algebraic Identities
If a + 1/a ...
Question
If
a
+
1
a
=
p
and
a
≠
0
; then show that:
a
3
+
1
a
3
=
p
(
p
2
−
3
)
Open in App
Solution
a
+
1
a
=
p
Squaring both sides
(
a
+
1
a
)
2
=
p
2
a
2
+
2
(
a
)
1
a
+
(
1
a
)
2
=
p
2
a
2
+
2
+
1
a
2
=
p
2
a
2
+
1
a
2
=
p
2
−
2
Now,
a
3
+
1
a
3
=
(
a
+
1
a
)
(
a
2
−
a
(
1
a
)
+
(
1
a
2
)
)
a
3
+
1
a
3
=
(
p
)
(
p
2
−
2
−
1
)
a
3
+
1
a
3
=
(
p
)
(
p
2
−
3
)
L
.
H
.
S
=
R
.
H
.
S
Suggest Corrections
0
Similar questions
Q.
State true or false:
If
a
+
1
a
=
p
and
a
≠
0
; then
a
3
+
1
a
3
=
p
(
p
2
−
3
)
Q.
If
a
+
1
a
=
p
and
a
≠
0
; then
a
3
+
1
a
3
is equal to