If a+1/a=6 and a ¥0;find:a^2-1/a^2
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Answer:
a−
a
1
=8
Squaring both sides,
=(a−
a
1
)
2
=8
2
=a
2
+(
a
1
)
2
−2(a)(
a
1
)=64
=a
2
+
a
2
1
−2=64
=a
2
+
a
2
1
=66
Now,
(a+
a
1
)
2
=a
2
+
a
2
1
+2(a)(
a
1
)
=66+2
=68
=>a+
a
1
=
68
=±2
1
7
Now,
a
2
−
a
2
1
=(a+
a
1
)(a−
a
1
)
=±(2
1
7)(8)
=±16
1
7
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