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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