Question 108

If $$a = x^{b - c}, b = x^{c - a}, c = x^{a - b}$$, then $$a^a.b^b.c^c =$$

Solution
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Given,

$$a = x^{b - c}$$

$$\Rightarrow$$  $$a^a=x^{ab-ac}$$ ........(1)

$$b = x^{c - a}$$

$$\Rightarrow$$  $$b^b=x^{bc-ba}$$ ........(2)

$$c = x^{a - b}$$

$$\Rightarrow$$  $$c^c=x^{ca-cb}$$ ........(3)

Now multiplying the equations (1), (2), (3)

$$a^a\ b^b\ c^c=x^{ab-ac+bc-ba+ca-cb}=x^0=1$$

Hence, the correct answer is Option B

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