Question 90

If $$x^{abc} = x^a.x^b.x^c$$, where $$a, b, c and x$$ are all positive integers, then what is the value of $$(a + b + c)^2$$?

Solution

Given : $$x^{abc} = x^a.x^b.x^c$$

=> $$x^{abc} = x^{(a+b+c)}$$

=> $$a+b+c=abc$$

$$\because$$ $$a,b,c$$ are all positive integers, the only numbers that can satisfy above equation are : $$a=1,b=2,c=3$$

To find : $$(a+b+c)^2=(6)^2=36$$

=> Ans - (D)

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