SOLUTION: If x^4+y^4=2 and x^8+y^8=3, what is the value of x^(16)+y^(16)

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Question 1086719: If x^4+y^4=2 and x^8+y^8=3, what is the value of x^(16)+y^(16)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
1.  If  = 2 then (squaring both sides)

        +  +  = 4.    (1)


    Using  = 3 (which is given) from (1) you get  = 1.    (2)


    Hence,   = .


2.  Now,  =  =  =  = .

Answer. = .


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
If x^4+y^4=2 and x^8+y^8=3, what is the value of x^(16)+y^(16)
 				  
 ------ Squaring both sides
 
 ------ Rearranging terms
 ------ Substituting 3 for  
 
 ------ eq (i)



 ------ Squaring both sides
 
 

 ------- Substituting ½ for

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