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Question

State true or false:

If (a+1a)2=3 and a0; then

a3+1a3=0

A
True
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B
False
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Solution

The correct option is A True
(a+1a)2=3
(a+1a)2=3
=>a2+1a2+2(a)(1a)=3
=>a2+1a2=32
=>a2+1a2=1
And
=>(a+1a)=3
Now,
=>a3+1a3=(a+1a)[(a2)+(1a2)(a)(1a)]
=3(11)
=0
Therefore,
L.H.S=R.H.S

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