Question

what is the sum of three​

Answer 1

Answer:

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Answer 2

Correct question :-

What is the sum of three​ cubes?

Solution :-

${\displaystyle a^{3}+(-a)^{3}+0^{3}=0.}$

${\displaystyle (9b^{4})^{3}+(3b-9b^{4})^{3}+(1-9b^{3})^{3}=1}{\displaystyle (9b^{4})^{3}+(3b-9b^{4})^{3}+(1-9b^{3})^{3}=1}$

${\displaystyle (1+6c^{3})^{3}+(1-6c^{3})^{3}+(-6c^{2})^{3}=2.}{\displaystyle (1+6c^{3})^{3}+(1-6c^{3})^{3}+(-6c^{2})^{3}=2.}$

These can be scaled to obtain representations for any cube or any number that is twice a cube.There exist other representations, and other parameterized families of representations, for 1. For 2, the other known representations are

${\displaystyle 1\ 214\ 928^{3}+3\ 480\ 205^{3}+(-3\ 528\ 875)^{3}=2,}$

${\displaystyle 37\ 404\ 275\ 617^{3}+(-25\ 282\ 289\ 375)^{3}+(-33\ 071\ 554\ 596)^{3}=2,}$

${\displaystyle 3\ 737\ 830\ 626\ 090^{3}+1\ 490\ 220\ 318\ 001^{3}+(-3\ 815\ 176\ 160\ 999)^{3}=2.}$

However, 1 and 2 are the only numbers with representations that can be parameterized by quartic polynomials in this way.

${\displaystyle 1^{3}+1^{3}+1^{3}=4^{3}+4^{3}+(-5)^{3}=3}$