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x² - 2x + 6 = 3x
x² - 2x - 3x +6 = 0
x² - 5x + 6 = 0 Factorizamos trinomio de la forma x² + bx + c
(x - 3)( x - 2) = 0 Tiene 2 soluciones reales
x - 3 = 0
x= 3
o
x - 2 = 0
x = 2
Respuesta.
x= 3
o
x = 2
x² - 2x + 6 = 3x
x² - 2x + 6 - 3x = 0
x² - 5x + 6 = 0
Factorizamos:
(x - 3).(x - 2) = 0
De aqui salen dos posibles respuestas:
x₁ => x - 3 = 0
x₁ = 3
x₂ => x - 2 = 0
x₂ = 2
Verificamos:
Con 3
x² - 2x + 6 = 3x
(3)² - 2(3) + 6 = 3(3)
9 - 6 + 6 = 9
9 = 9
Con 2
x² - 2x + 6 = 3x
(2)² - 2(2) + 6 = 3(2)
4 - 4 + 6 = 6
6 = 6
Igualdad Verdadera
Espero ayude