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Kurma Anudeep Grade: 10
        1. If (x+iy)^1/3=a+ib, x,y,a,b E R.Show that x/a+y/b=4(a^2-b^2)
4 years ago

Answers : (1)

Aman Bansal
592 Points
										

Dear Kurma,


after cubing given eqn we get


 


 x+iy=a^3-ib^3+3aib(a+ib)


 


       =a^3-ib^3+3a^2ib-3ab^2


 


      =a^3-3ab^2+i(3a^2b-b^3)    


 


comparing


 


x=a^3-3ab^2,y=3a^2b-b^3


 


x/a+y/b=a^2-3b^2+3a^2-b^2


 


          =4(a^2-b^2)


 


proved 


 


hope i helped u


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Aman Bansal


Askiitian Expert

4 years ago
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