Question

Is {x : x² – 5x – 6 = 0} = {2, 3} ?

Answer 1

x⁵ - 5x - 6 = 0
⇒ x² - 6x + x - 6 = 0
⇒ x (x - 6) + 1 (x - 6) = 0
⇒ (x - 6) (x - 1) = 0
∴ Either x - 6 = 0 
i.e., x = 6
Or
x + 1 = 0
i.e. x = -1
∴ {x : x² - 5x - 6 = 0} ≠ {2, 3}
In other words {x : x² - 5x -6 = 0}
= {2, 3} is not true.