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  • Find all real numbers satisfying x^8+y^8=8xy-6

Find all real numbers satisfying x^8+y^8=8xy-6

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Solution:   We know ,  x^8+y^8=8xy-6

         \ \ Rightarrow x^8+y^8+6=8xy\ \ Rightarrow x^8+y^8+1+1+1+!+1+1=8xyhspace0.5cm..........(1)   

            By , AMgeq GM

                    fracx^8+y^8+1+1+1+1+1+18geq (x^8y^8)^frac18

                      x^8+y^8+6geq 8xy hspace0.5cm..........(2)

  From Equation  (1)  and  (2) equality holds  when all terms

are equal    i.e   x^8=y^8=1

   Hence ,      x=pm 1,y=pm1  is the solution set.

Posted by

Deependra Verma

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