Schultz Sherman
09/18/2024 · Middle School
Señala el C.S., luego de resolver: \[ x^{2}=x+3 \]
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Tutor-Verified Answer
Step-by-step Solution
Para resolver la ecuación \( x^{2} = x + 3 \), primero la reorganizamos para que todos los términos estén de un lado de la ecuación:
\[
x^{2} - x - 3 = 0
\]
Ahora, podemos aplicar la fórmula general para resolver ecuaciones cuadráticas, que es:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
En nuestra ecuación, los coeficientes son:
- \( a = 1 \)
- \( b = -1 \)
- \( c = -3 \)
Sustituyendo estos valores en la fórmula:
1. Calculamos el discriminante \( b^2 - 4ac \):
\[
(-1)^2 - 4(1)(-3) = 1 + 12 = 13
\]
2. Ahora sustituimos en la fórmula:
\[
x = \frac{-(-1) \pm \sqrt{13}}{2(1)} = \frac{1 \pm \sqrt{13}}{2}
\]
Por lo tanto, las soluciones son:
\[
x_1 = \frac{1 + \sqrt{13}}{2} \quad \text{y} \quad x_2 = \frac{1 - \sqrt{13}}{2}
\]
El conjunto solución (C.S.) es:
\[
\left\{ \frac{1 + \sqrt{13}}{2}, \frac{1 - \sqrt{13}}{2} \right\}
\]
Quick Answer
El conjunto solución (C.S.) es: \(\left\{ \frac{1 + \sqrt{13}}{2}, \frac{1 - \sqrt{13}}{2} \right\}\)
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