3. If a+ 1/a = 6, find a-1/a
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Answer:
a+
a
1
=6
Squaring both sides,
=(a+
a
1
)
2
=6
2
=a
2
+(
a
1
)
2
+2(a)(
a
1
)=36
=a
2
+
a
2
1
+2=36
=a
2
+
a
2
1
=34
Now,
(a−
a
1
)
2
=a
2
+
a
2
1
−2(a)(
a
1
)
=34−2
=32
=>a−
a
1
=±
32
=±4
2
Now,
(a
2
−
a
2
1
)=(a+
a
1
)(a−
a
1
)
=6(±4
2
)
=±24
2
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