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Question

If x=526, find x2+1x2.

Solution
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We know, x2+1x2=(x1x)2+2
Given, x=526.
Then, 1x=1526=5+26(526)(5+26)=5+2652(26)2=5+262524=5+261=5+26.
Then, x2+1x=(526(5+26))2+2
(46)2+2=96+2=98.
Therefore, the required value is 98.

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