Respuesta :
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