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5. Given [tex]\( a + 2 = a^2 + 2 \)[/tex], calculate [tex]\( 3 + 4 + 5 \)[/tex].

A) 2
B) 0
C) -1
D) -2
E) -3

Sagot :

GinnyAnswer
Para resolver la ecuación [tex]\(a + 2 = a^2 + 2\)[/tex], primero vamos a despejar [tex]\(a\)[/tex].

Empezamos simplificando la ecuación:

[tex]\[ a + 2 = a^2 + 2 \][/tex]

Restando 2 de ambos lados, obtenemos:

[tex]\[ a = a^2 \][/tex]

Restando [tex]\(a\)[/tex] de ambos lados, tenemos:

[tex]\[ 0 = a^2 - a \][/tex]

Factorizamos:

[tex]\[ 0 = a(a - 1) \][/tex]

Entonces, tenemos dos soluciones posibles para [tex]\(a\)[/tex]:

[tex]\[ a = 0 \quad \text{o} \quad a = 1 \][/tex]

Ahora, según el problema, una vez resuelta la ecuación, nos piden calcular [tex]\(3 + 4 + 5\)[/tex].

Simplemente sumamos estos números:

[tex]\[ 3 + 4 + 5 = 12 \][/tex]

Por lo tanto, la respuesta correcta es:

[tex]\[ \boxed{12} \][/tex]
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