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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.

 Jul 23, 2021
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x^2  + y^2   =  1      square both sides

 

(x^4  + 2(xy)^2  + y^4)   = 1

 

(x^4 + y^4)   +  2 (xy)^2    =1

 

(17/19)  +  2(xy)^2  = 1

 

2(xy)^2  =    1   -17/19

 

2 (xy)^2  =      2 / 19         divide both sides  by 2

 

(xy)^2   =   1 /19

 

xy  =  sqrt (1/19) = sqrt (19) / 19

 

cool cool cool

CPhill Jul 23, 2021

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