Question

x+y verises x-y then prove that x^3+y^3 verises xy(x+y) ​

Answer 1

(x+y)

prop

(x-y)

rArr (x+y)

=k (x-y) (where k

ne

0= variation constant ) <br>

rArr (x+y)/(x-y)=k

<br>

rArr (x+y+x-y)/(x+y-x+y)=(k+1)/(k-1)

[by componendo and dividendo] <br>

rArr (2x)/(2y)=(k+1)/(k-1)rArr(x)/(y)=(k+1)/(k-1)=m("let") [when (k+1)/(k-1)=m]

<br>

rArr (x/y)^(3) =m^(3)

(cubing both the sides )<br>

rArr x^(3)/y^(3)=m^(3)rArr (x^(3)+y^(3))/(x^(3)-y^(3))=(m^(3)+1)/(m^(3)-1)

[by componendo and dividendo] <br>

(x^(3)+y^(3))/(x^(3)-y^(3))=n ["whene" n =(m^(3)+1)/(m^(3)-1)ne0]

<br>

x^(3)+y^(3) =n(x^(3)-y^(3)) and n ne0="variation constant."

<br>

(x^(3)+y^(3))prop(x^(3)-y^(3))(proved)

plese mark me as a brenllist