a^3 + b^3 = (10)(58 - 21) = 10 \times 37 = 370
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- 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:
- Por lo tanto, el valor de $a^3 + b^3$ es $\boxed{370}$.
- Pregunta: Si $x + y = 5$ y $xy = 6$, encuentra el valor de $x^2 + y^2$.
- Usamos la identidad:
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