perplexus.info :: Just Math : Cubic conundrum

Cubic conundrum (Posted on 2021-10-18)

Let x, y be real numbers other than 0 that satisfy x³+y³+3x²y²=x³y³. Find all possible values of 1/x+1/y.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (1 votes)

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Solution

| Comment 1 of 3

A graph of the equation appears to form the hyperbola 1/x+1/y=1 or y=x/(x-1).

Making this substitution into the LHS and RHS of the equations yields the same thing: x^6/(x-1)^3

Posted by Jer on 2021-10-19 07:44:49

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