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Las soluciones son x = 1 y x = 2.
Solution
Vamos a resolver la ecuación cuadrática:
x² - 3x + 2 = 0
Paso 1: Factorizar la ecuación. Se busca escribirla en la forma (x - a)(x - b) = 0, donde a y b son números tales que:
a + b = 3 (ya que - (a + b) = -3)
a · b = 2
Observamos que los números 1 y 2 cumplen: 1 + 2 = 3 y 1 · 2 = 2.
Por lo tanto, la ecuación se factoriza como:
(x - 1)(x - 2) = 0
Paso 2: Hallar las soluciones igualando cada factor a cero.
Si:
x - 1 = 0 => x = 1
y
x - 2 = 0 => x = 2
Conclusión: Las soluciones de la ecuación son x = 1 y x = 2.
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Simplify this solution Extra Insights
To solve the equation \( x^{2}-3x+2=0 \), you can use factoring! This quadratic can be factored into \( (x-1)(x-2)=0 \). From here, set each factor equal to zero, giving you the solutions \( x=1 \) and \( x=2 \). Voilà, you have your two solutions! Now, did you know that quadratic equations like this one appear everywhere in our lives? They can model everything from projectile motion in sports—think about a basketball shot—to optimizing profits in business! Understanding how to solve them can really be a game-changer for your analytical skills.
