if (a²+1/a²) =27 , find the value of (i) (a-1/a) (ii) (a³-1/a³)
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Answer:
a
2
+
a
2
1
=18
(a−
a
1
)
2
=a
2
+
a
2
1
−2
⇒(a−
a
1
)
2
=18−2
⇒(a−
a
1
)
2
=16
⇒(a−
a
1
)=±
16
⇒(a−
a
1
)=±4......(1)
(a−
a
1
)
3
=a
3
−
a
3
1
−3×a×
a
1
(a−
a
1
)
⇒a
3
−
a
3
1
=(a−
a
1
)
3
+3(a−
a
1
)
⇒a
3
−
a
3
1
=(±4)
3
+3(±4) [From (1)]
⇒a
3
−
a
3
1
=±76
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