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Question

If a+1a=6 and a0; find a21a2 .

A
±243
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B
±42
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C
±242
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D
±43
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Solution

The correct option is D ±242
a+1a=6
Squaring both sides,
=(a+1a)2=62
=a2+(1a)2+2(a)(1a)=36
=a2+1a2+2=36
=a2+1a2=34
Now,
(a1a)2=a2+1a22(a)(1a)
=342
=32
=>a1a=±32
=±42
Now,
(a21a2)=(a+1a)(a1a)
=6(±42)
=±242

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