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Question 19
If $$x_1x_2x_3 = 4(4 + x_1 + x_2 + x_3),$$ then what is the value of $$\left[\frac{1}{(2 + x_1)}\right] + \left[\frac{1}{(2 + x_2)}\right] + \left[\frac{1}{(2 + x_3)}\right]$$?
Solution
$$x_1x_2x_3 = 4(4 + x_1 + x_2 + x_3),$$
From clear observation we can say that $$x_1=4,x_2=4,x_3=4 $$ will satisfy the equation
i.e 4*4*4=4(4+12)
64=64
Therefore $$\left[\frac{1}{(2 + x_1)}\right] + \left[\frac{1}{(2 + x_2)}\right] + \left[\frac{1}{(2 + x_3)}\right]$$=3(1/6)
=1/2
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