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If $$\frac{{2 + a}}{a}$$ + $$\frac{{2 + b}}{b}$$ + $$\frac{{2 + c}}{c}$$ = 4, then the value of $$\frac{{ab + bc + ca}}{{abc}}$$ is?
Answer & Solution
Correct Answer:
Option
D
$$\eqalign{
& \frac{{2 + a}}{a} + \frac{{2 + b}}{b} + \frac{{2 + c}}{c} = 4 \cr
& \Rightarrow \frac{{2bc + abc + 2ac + abc + 2ab + abc}}{{abc}} = 4 \cr
& \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + \frac{{3abc}}{{abc}} = 4 \cr
& \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + 3 = 4 \cr
& \Rightarrow \boxed{\frac{{ab + bc + ca}}{{abc}} = \frac{1}{2}} \cr} $$
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