Question

I cannot understand this AT ALL (would be glad to have an explanation)

Answer 1

hmmm well, don't be so hmmm off due to it, the wording in the exercise sux0rs bad, is very poorly worded and laid out.

if X and Y are numbers, hmmm say let's give them hmmm ohhh X = 7 and Y = 13.

And X and Y are also complete cubes, well, let's make them so, X = 7³ and Y = 13³.

which of those expressions are complete cubes, or namely, something that we can write as a number with a "3" in the exponent, let's check each one.

`\begin{array}l 8X&\implies 8\cdot 7^3& 2^3\cdot 7^3& (2\cdot 7)^3& 14^3 ~~ \checkmark\\&&&&\\ X,Y&\implies 7^3,13^3 ~~ \checkmark&&\\&&&&\\ -X&\implies -7^3~~ \checkmark&&\\&&&&\\ 27XY&\implies 27\cdot 7^3\cdot 13^3& 3^3\cdot 7^3\cdot 13^3& (3\cdot 7\cdot 13)^3& 273^3~~ \checkmark\\&&&&\\ XY+27&\implies 7^3\cdot 13^3+27&(7\cdot 13)^3 + 3^3&&91^3+3^3 ~~ \bigotimes \end{array}`

what's wrong with the last one? well, if we were to add 91³ + 3³ = 753598. Now, is 753598 a complete cube? well, only if we could write it as a whole number with a "3" above, can we? nope.

we can simply check that by getting the 3rd root of that value,

`\sqrt[3]{753598}\approx 91.00108681228277\impliedby \textit{not a complete cube}`