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Find x + y if the pair\( (x,y)satisfies x^4=y^4+18\sqrt3,x^2+y^2=6, and x+y=3.\)

Guest Feb 16, 2018
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avatar+86649 
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We already know that x + y   = 3  .....  do you mean x  - y  ???

 

x^4 = y^4 + 18√3,  x^2 + y^2  =  6,  x + y  =  3

 

Using the first equation

 

x^4 - y^4  = 18√3      factor the left side

 

(x^2  - y^2) (x^2 + y^2)  =18√3        sub in the second equation

 

(x^2 - y^2) (6)  =  18√3      divide both sides  by 6

 

(x^2  - y^2)  = 3√3    factor again  

 

( x - y) (x + y)  = 3√3  sub in the third equation

 

(x - y)  (3)  =  3√3    divide both sides by 3

 

x  - y   =  √3

 

 

cool cool cool

CPhill  Feb 16, 2018

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