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Pell's Equation

Solve .Give 3 positive solutions.

First step:
Find the continued expansion of




thus,

Second step:
Since n=2 and it is even, the solutions are
where k=1,2,3...
Thus,



.
.
.
are the positive solutions.

Third step:
Calculate the value of the numerator and denominator,







So,the answers for 3 positive solutions of are


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