In the given question, we are given a © b as the operation defined as ab + ba. We need to find the value of x in each option and determine which option has the smallest value of x.
Let`s solve each option one by one:
Option 1: I 2 © x = 100
Plugging in the values, we get 2x + x2 = 100
By rearranging the equation, we get x2 + 2x - 100 = 0
By solving this quadratic equation, we find that x = 10 or x = -12.
Therefore, x can be either 10 or -12.
Option 2: II 4 © x = 145
Using the same logic as before, we get 4x + x4 = 145
Simplifying, we get x4 + 4x - 145 = 0
By solving this equation, we find that x is approximately 7.4.
Option 3: III 3 © x = 145
Similarly, we get 3x + x3 = 145
Simplifying, we get x3 + 3x - 145 = 0
By solving this equation, we find that x