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Question

If the value of a+1a=3, then the value of a4+1a4 is equal to.

A
45
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B
47
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C
49
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D
51
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Solution

The correct option is B 47
It is given that a+1a=3
Using identity,
(a+b)2=a2+2ab+b2,
we have
a2+1a2=(a+1a)22
a2+1a2=322
a2+1a2=92
a2+1a2=7

Squaring both sides we get,

(a2+1a2)2=72
(a2)2+(1a2)2+2(a2)(1a2)=72
a4+1a4+2=49
a4+1a4=47

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