Respuesta :

genan

Answer:

The set solution is [1,4]

Step-by-step explanation:

To find the solution set

Expand,

(x - 2)(x - 3) =

  • x times x = x²
  • x times -2 = -2x
  • x times -3 = -3x
  • -2 times -3 = 6
  • -2x + (-3x) = -5x

Now, x² - 5x + 6 = 2

we want the right to be = 0 so subtract 2 from both sides

x² - 5x + 6 - 2 = 2 - 2

x² - 5x + 4 = 0

we can now use the quadratic formula,

  • [tex]x = \frac{-b+\sqrt{b^{2}-4ac} }{2a}[/tex]
  • ax² + bx + c = 0
  • a = 1
  • b = -5
  • c = 4

[tex]x = \frac{-(-5)+\sqrt{(-5)^{2}-4*1*4 } }{2*1}[/tex]

[tex]x = \frac{(5)+\sqrt{(25)-4*4 } }{2}[/tex][tex]= \frac{(5)+\sqrt{(25)-16 } }{2}[/tex][tex]= \frac{(5)+\sqrt{9} }{2}[/tex]

[tex]x = \frac{(5)+3 }{2}[/tex]   = 4

[tex]x = \frac{(5)-3 }{2} \\[/tex]   = 1

Hence the set solution is [1,4]

Learn more about Quadratic Formula here: https://brainly.com/question/1214333

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