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Home » Final Answer:** $ \boxed27 $ - Esdistancia

Final Answer:** $ \boxed27 $ - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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x^3 + y^3 = (x + y)(x^2 - xy + y^2) = 6(20 - 8) = 6 \times 12 = 72
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:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
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...
Sustituimos en la identidad:
a^3 + b^3 = (10)(58 - 21) = 10 \times 37 = 370
Por lo tanto, el valor de $a^3 + b^3$ es $\boxed{370}$.

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