Question 1086719
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1.  If {{{x^4 + y^4}}} = 2 then (squaring both sides)

       {{{x^8}}} + {{{2x^4*y^4}}} + {{{y^8}}} = 4.    (1)


    Using {{{x^8+y^8}}} = 3 (which is given) from (1) you get {{{2x^4*y^4}}} = 1.    (2)


    Hence,  {{{x^4*y^4}}} = {{{1/2}}}.


2.  Now, {{{x^16 + y^16}}} = {{{(x^8+y^8)^2 - 2x^8*y^8}}} = {{{3^2 - 2*(x^8*y^8)}}} = {{{9 - 2*(1/2)^2}}} = {{{8}}}{{{1/2}}}.
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<U>Answer</U>.  {{{x^16 + y^16}}} = {{{8}}}{{{1/2}}}.