a good problem on exponents

Algebra Level pending

if a<n>= (x^(1/2)^n) +(y^(1/2)^n)
if b<n>= (x^(1/2)^n) - (y^(1/2)^n) for n=1,2,3......... then a<1>.a<2>.a<3>...............a<n>=

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