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3x cubed + 2y cubed = z cubed

2x cubed + 5y cubed = z cubed

Since these two equations are clearly not dependent, could we say that since they both are equal to the same term (z cubed), that they are therefore, inconsistent?

- Thread starter e2m2a
- Start date

- 270

- 3

3x cubed + 2y cubed = z cubed

2x cubed + 5y cubed = z cubed

Since these two equations are clearly not dependent, could we say that since they both are equal to the same term (z cubed), that they are therefore, inconsistent?

Mentor

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Both left hand sides are equal to the same thing, which means ##3x^2+2y^3=2x^3+5y^3##, that is an equation with solutions. An infinite set of solutions, actually. And for every solution of that equation there is a z that fits.

If you can derive something impossible, (like ##x^2=-1## if you work with real numbers), then there is no solution, but it is not always directly obvious if you can do that.

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They are not "inconsistent" which presumable means "without solution". Those kind of questions define an algebraic variety and are subject to commutative algebra and algebraic geometry. As far as I know, there is no test in "P" that decides the shape of the zeros, but this is more of a guess.

3x cubed + 2y cubed = z cubed

2x cubed + 5y cubed = z cubed

Since these two equations are clearly not dependent, could we say that since they both are equal to the same term (z cubed), that they are therefore, inconsistent?

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