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Positive real numbers x, y satisfy the equations x^2 + y^2 = 1 and x^4 + y^4 = 17/19. Find xy.

 Feb 26, 2022
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Start with this:

 

(x^2 + y^2 ) 2   = ( x^4  + y^4)    +   2 x^2 y^2        now remember    x^2 + y^2 = 1    so

       1              =   17/19          + 2 x^2 y^2            I think you should be able to finish from here, yah?

 Feb 26, 2022

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