Question 75

If $$a * b = a + b - \frac{ab}{2}\forall a, b \epsilon R$$ and if c is a non-zero real number, then the value of x satisfying x * c = x is

Solution

Given, $$a * b = a + b - \frac{ab}{2}$$

If x * c = x

$$\Rightarrow$$ x + c - $$\frac{\text{xc}}{2}$$ = x

$$\Rightarrow$$ c - $$\frac{\text{xc}}{2}$$ = 0

$$\Rightarrow$$ $$\frac{\text{xc}}{2}$$ = c

$$\Rightarrow$$ x = 2

$$\therefore\ $$The value of x satisfying x * c = x is x = 2

Hence, the correct answer is Option B

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