If a b is defined as ab + ba, then consider : I 2 x = 100 II 4 x = 145 III 3 x = 145 IV 6 x = 100 For which of the above, is x smallest ?

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Q: 111 (CAPF/2009)
If a © b is defined as ab + ba, then consider : I 2 © x = 100 II 4 © x = 145 III 3 © x = 145 IV 6 © x = 100 For which of the above, is x smallest ?

question_subject: 

Science

question_exam: 

CAPF

stats: 

0,0,5,2,2,1,0

keywords: 

{'ab': [0, 0, 1, 0], 'ba': [1, 0, 1, 1], 'iv': [6, 110, 77, 8]}

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