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Sagot :
Vamos a resolver el problema paso a paso utilizando las expresiones algebraicas proporcionadas.
1. Datos proporcionados:
- [tex]\(a^2 + b^2 + c^2 = 35\)[/tex]
- [tex]\(ab + bc + ca = 23\)[/tex]
2. Queremos encontrar [tex]\((a + b + c)^2\)[/tex].
3. Recordamos la identidad algebraica:
[tex]\[ (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) \][/tex]
4. Sustituimos los valores dados en la identidad algebraica:
[tex]\[ (a + b + c)^2 = 35 + 2(23) \][/tex]
5. Calculamos [tex]\(2 \times 23\)[/tex]:
[tex]\[ 2 \times 23 = 46 \][/tex]
6. Sumamos los términos:
[tex]\[ (a + b + c)^2 = 35 + 46 \][/tex]
7. Finalmente, obtenemos:
[tex]\[ (a + b + c)^2 = 81 \][/tex]
Por lo tanto, el valor numérico de [tex]\((a + b + c)^2\)[/tex] es 81.
1. Datos proporcionados:
- [tex]\(a^2 + b^2 + c^2 = 35\)[/tex]
- [tex]\(ab + bc + ca = 23\)[/tex]
2. Queremos encontrar [tex]\((a + b + c)^2\)[/tex].
3. Recordamos la identidad algebraica:
[tex]\[ (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) \][/tex]
4. Sustituimos los valores dados en la identidad algebraica:
[tex]\[ (a + b + c)^2 = 35 + 2(23) \][/tex]
5. Calculamos [tex]\(2 \times 23\)[/tex]:
[tex]\[ 2 \times 23 = 46 \][/tex]
6. Sumamos los términos:
[tex]\[ (a + b + c)^2 = 35 + 46 \][/tex]
7. Finalmente, obtenemos:
[tex]\[ (a + b + c)^2 = 81 \][/tex]
Por lo tanto, el valor numérico de [tex]\((a + b + c)^2\)[/tex] es 81.
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