a^3 + b^3 = (a + b)(a^2 - ab + b^2)
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- Por lo tanto, el valor de $x^3 + y^3$ es $\boxed{72}$.
- Pregunta: Si $a + b = 10$ y $a^2 + b^2 = 58$, encuentra $a^3 + b^3$.
- Usamos la identidad para la suma de cubos:
- Sabemos $a + b = 10$ y $a^2 + b^2 = 58$. Para encontrar $ab$, usamos:
- 10^2 = 58 + 2ab \implies 100 = 58 + 2ab \implies 2ab = 42 \implies ab = 21
- Sustituimos en la identidad:
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