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3. Si [tex]$a^2 \# b^2=2ab - a + b$[/tex], halla [tex](25 \# 36) - (16 \# 9)[/tex].

Sagot :

GinnyAnswer
Para resolver la expresión \((25 \# 36) - (16 \# 9)\) utilizando la operación definida \( a^2 \# b^2 = 2ab - a + b \), sigamos estos pasos:

1. Primero, calculemos \( 25 \# 36 \):
- Identifiquemos \( a \) y \( b \) en la operación: \( a = 25 \) y \( b = 36 \).
- Sustituyamos en la fórmula: \( 25^2 \# 36^2 = 2 \cdot 25 \cdot 36 - 25 + 36 \).
- Realicemos la multiplicación: \( 2 \cdot 25 \cdot 36 = 1800 \).
- Ahora, combinen todo: \( 1800 - 25 + 36 = 1800 - 25 + 36 = 1811 \).

Por lo tanto, el resultado de \( 25 \# 36 \) es 1811.

2. Ahora, calculemos \( 16 \# 9 \):
- Identifiquemos \( a \) y \( b \) en la operación: \( a = 16 \) y \( b = 9 \).
- Sustituyamos en la fórmula: \( 16^2 \# 9^2 = 2 \cdot 16 \cdot 9 - 16 + 9 \).
- Realicemos la multiplicación: \( 2 \cdot 16 \cdot 9 = 288 \).
- Ahora, combinen todo: \( 288 - 16 + 9 = 288 - 16 + 9 = 281 \).

Por lo tanto, el resultado de \( 16 \# 9 \) es 281.

3. Finalmente, sustraigamos los resultados obtenidos:
- \( (25 \# 36) - (16 \# 9) = 1811 - 281 \).
- Realicemos la resta: \( 1811 - 281 = 1530 \).

Por lo tanto, el resultado de [tex]\((25 \# 36) - (16 \# 9)\)[/tex] es 1530.
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