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If (x+y)/(x-y)=3, what is [(x^3+y^3)/(x^3-y^3)][(x^2+y^2)/(x^2-y^2)][(x+y)/(x-y)]?

If (x+y)/(x-y)=3, what is [(x^3+y^3)/(x^3-y^3)][(x^2+y^2)/(x^2-y^2)][(x+y)/(x-y)]?


 

Grade:12

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Red Dane,

 

This problem would require a little bit of manupilation of the given condition (a good trick).

 

As (x+y)/(x-y) = 3 we will have 3x+3y = x-y or 2x=4y or x/y=2....

So with x/y=2,

The required expression is:

[ {(x/y)3+1}/{(x/y)3-1} ] [ {(x/y)2+1}/{(x/y)2-1} ] [ {(x/y)+1}/{(x/y)-1} ].

Substitute for x/y = 2, and get the answer.

It will be 9/7 * 5/3 * 3 = 45/7.

 

Hope it helps.

Wish you all the best.

 

Regards,

Ashwin (IIT MadraS).

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