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Question

If x+1x=4 then x5+1x5=?

A
723
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B
724
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C
725
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D
726
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Solution

The correct option is C 724
Given,
x+1x=4......(1).
Now squaring both sides we get,
x2+2+1x2=16
or, x2+1x2=14.......(2).
Now again cubing equation (1) we get,
x3+3.x.1x(x+1x)+1x3=64
or, x3+1x3=6412
or, x3+1x3=52.......(3).
Now multiplying (2) and (3) we get,
x5+x+1x+1x5=728
or, x5+1x5=7284=724. [ Using (1)].

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