Mathematics, 22.07.2019 21:30 carlosatniel47
What is 125x9 + 64y12 written as a sum of cubes?
Answers: 1
![\bf 125x^9+64y^{12}\qquad \begin{cases} 125=5\cdot 5\cdot 5\\ \qquad 5^3\\ x^9=x^{3\cdot 3}\\ \qquad (x^3)^3\\ 64=4\cdot 4\cdot 4\\ \qquad 4^3\\ y^{12}=y^{4\cdot 3}\\ \qquad (y^4)^3 \end{cases}\implies 5^3(x^3)^3+4^3(y^4)^3 \\\\\\ (5x^3)^3+(4y^4)^3\implies [(5x^3)^2-(5x^3)(4y^4)+(4y^4)^2] \\\\\\ 25x^6-20x^3y^4+16y^8](/tpl/images/0120/9999/01be8.png)
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