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Question

If (1x)(1+x+x2+x3+x4) is 3132 and x is a rational number. FInd the value of 1+x+x2+x3+x4+x5.


Solution

(1x)(1+x+x2+x3+x4)=3132
1+x+x2+x3+x4=1x51x
(1x)(1x51x)=3132 or x5=13132.132
or x=1532=12
1+x+x2+x3+x4+x5=1x61x=1126112=116412=2×6364=6332

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