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Given Real Numbers, Find all possible Sums (Posted on 2024-05-04)

Each of x and y is a real number that satisfies this equation:

x³ + y³ + 8 = 6xyz

Find all possible values of x+y

No Solution Yet Submitted by K Sengupta

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solution (spoiler)

| Comment 1 of 2

Since

z = (x^3 + y^3 + 8) / (6*x*y)

the only restriction on x and y is that neither can be zero.

But that doesn't prevent x + y from being any real value whatsoever. The value of x + y can be zero so long as x = -y not= 0.

Posted by Charlie on 2024-05-04 09:00:34

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