Binomial Cubed!

Algebra Level 3

If x y + y x = 3 \dfrac{x}{y} + \dfrac{y}{x} = 3 , find the value of x 3 y 3 + y 3 x 3 \dfrac{x^3}{y^3} + \dfrac{y^3}{x^3} .


The answer is 18.

Mohamed Aly by Mohamed Aly , 49, Egypt

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1 solution

Mohamed Aly
Mar 7, 2017

6 Helpful 0 Interesting 0 Brilliant 0 Confused

An Alternative way could have been using the identity x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) \large x^{3}+y^{3}= (x+y)(x^{2}-xy+y^{2})

Achal Jain - 4 years, 3 months ago

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