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Sagot :
Para resolver el problema [tex]\( [P(-1)]^{P(1)} \)[/tex], primero necesitamos evaluar el polinomio [tex]\( P(x) = 5x^2 + 7x - 12 \)[/tex] en [tex]\( x = -1 \)[/tex] y [tex]\( x = 1 \)[/tex].
1. Evaluando [tex]\( P(-1) \)[/tex]:
[tex]\[ P(-1) = 5(-1)^2 + 7(-1) - 12 \][/tex]
Calculamos cada término:
[tex]\[ (-1)^2 = 1 \][/tex]
[tex]\[ 5 \cdot 1 = 5 \][/tex]
[tex]\[ 7 \cdot (-1) = -7 \][/tex]
Ahora sumamos estos resultados:
[tex]\[ P(-1) = 5 - 7 - 12 = -14 \][/tex]
2. Evaluando [tex]\( P(1) \)[/tex]:
[tex]\[ P(1) = 5(1^2) + 7(1) - 12 \][/tex]
Calculamos cada término:
[tex]\[ 1^2 = 1 \][/tex]
[tex]\[ 5 \cdot 1 = 5 \][/tex]
[tex]\[ 7 \cdot 1 = 7 \][/tex]
Ahora sumamos estos resultados:
[tex]\[ P(1) = 5 + 7 - 12 = 0 \][/tex]
3. Calculando [tex]\( [P(-1)]^{P(1)} \)[/tex]:
[tex]\[ [P(-1)]^{P(1)} = (-14)^0 \][/tex]
Cualquier número elevado a la potencia de 0 es igual a 1:
[tex]\[ (-14)^0 = 1 \][/tex]
Por lo tanto, el resultado final es:
[tex]\[ [P(-1)]^{P(1)} = 1 \][/tex]
Resumen:
1. [tex]\( P(-1) = -14 \)[/tex]
2. [tex]\( P(1) = 0 \)[/tex]
3. [tex]\( (-14)^0 = 1 \)[/tex]
Entonces, el resultado de [tex]\( [P(-1)]^{P(1)} \)[/tex] es [tex]\( 1 \)[/tex].
1. Evaluando [tex]\( P(-1) \)[/tex]:
[tex]\[ P(-1) = 5(-1)^2 + 7(-1) - 12 \][/tex]
Calculamos cada término:
[tex]\[ (-1)^2 = 1 \][/tex]
[tex]\[ 5 \cdot 1 = 5 \][/tex]
[tex]\[ 7 \cdot (-1) = -7 \][/tex]
Ahora sumamos estos resultados:
[tex]\[ P(-1) = 5 - 7 - 12 = -14 \][/tex]
2. Evaluando [tex]\( P(1) \)[/tex]:
[tex]\[ P(1) = 5(1^2) + 7(1) - 12 \][/tex]
Calculamos cada término:
[tex]\[ 1^2 = 1 \][/tex]
[tex]\[ 5 \cdot 1 = 5 \][/tex]
[tex]\[ 7 \cdot 1 = 7 \][/tex]
Ahora sumamos estos resultados:
[tex]\[ P(1) = 5 + 7 - 12 = 0 \][/tex]
3. Calculando [tex]\( [P(-1)]^{P(1)} \)[/tex]:
[tex]\[ [P(-1)]^{P(1)} = (-14)^0 \][/tex]
Cualquier número elevado a la potencia de 0 es igual a 1:
[tex]\[ (-14)^0 = 1 \][/tex]
Por lo tanto, el resultado final es:
[tex]\[ [P(-1)]^{P(1)} = 1 \][/tex]
Resumen:
1. [tex]\( P(-1) = -14 \)[/tex]
2. [tex]\( P(1) = 0 \)[/tex]
3. [tex]\( (-14)^0 = 1 \)[/tex]
Entonces, el resultado de [tex]\( [P(-1)]^{P(1)} \)[/tex] es [tex]\( 1 \)[/tex].
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