Q6 of 37 Page 195

If x + y ∝ x – y, let us show that

x3 + y3∝ x3 – y3

Given: x + y ∝ x – y

It can be written as,


x + y = k(x – y)



Apply componendo dividend,





Cube on both sides,



Again apply componendo dividend,



i.e. x3 + y3∝ x3 - y3


Hence,


x3 + y3∝ x3 - y3


Hence proved.


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