2+aa2+aa\frac{{2 + a}}{a} + 2+bb" role="presentation">2+bb2+bb\frac{{2 + b}}{b} + 2+cc" role="presentation">2+cc2+cc\frac{{2 + c}}{c} = 4, then the value of ab+bc+caabc" role="presentation">ab+bc+caabcab+bc+caabc\frac{{ab + bc + ca}}{{abc}} is?" /> 2+aa2+aa\frac{{2 + a}}{a} + 2+bb" role="presentation">2+bb2+bb\frac{{2 + b}}{b} + 2+cc" role="presentation">2+cc2+cc\frac{{2 + c}}{c} = 4, then the value of ab+bc+caabc" role="presentation">ab+bc+caabcab+bc+caabc\frac{{ab + bc + ca}}{{abc}} is?" /> 2+aa2+aa\frac{{2 + a}}{a} + 2+bb" role="presentation">2+bb2+bb\frac{{2 + b}}{b} + 2+cc" role="presentation">2+cc2+cc\frac{{2 + c}}{c} = 4, then the value of ab+bc+caabc" role="presentation">ab+bc+caabcab+bc+caabc\frac{{ab + bc + ca}}{{abc}} is?" />

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If $\frac{2 + a}{a}$ $\frac{{2 + a}}{a}$ + $\frac{2 + b}{b}$ $\frac{{2 + b}}{b}$ + $\frac{2 + c}{c}$ $\frac{{2 + c}}{c}$ = 4, then the value of $\frac{a b + b c + c a}{a b c}$ $\frac{{ab + bc + ca}}{{abc}}$ is?

12
21
30
4 $\frac{1}{2}$ $\frac{1}{2}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{2 + a}{a} + \frac{2 + b}{b} + \frac{2 + c}{c} = 4 \\ \Rightarrow \frac{2 b c + a b c + 2 a c + a b c + 2 a b + a b c}{a b c} = 4 \\ \Rightarrow \frac{2 (b c + a b + c a)}{a b c} + \frac{3 a b c}{a b c} = 4 \\ \Rightarrow \frac{2 (b c + a b + c a)}{a b c} + 3 = 4 \\ \Rightarrow \frac{a b + b c + c a}{a b c} = \frac{1}{2} \end{aligned}

$\eqalign{ & \frac{{2 + a}}{a} + \frac{{2 + b}}{b} + \frac{{2 + c}}{c} = 4 \cr & \Rightarrow \frac{{2bc + abc + 2ac + abc + 2ab + abc}}{{abc}} = 4 \cr & \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + \frac{{3abc}}{{abc}} = 4 \cr & \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + 3 = 4 \cr & \Rightarrow \boxed{\frac{{ab + bc + ca}}{{abc}} = \frac{1}{2}} \cr}$

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+

\frac{2 + b}{b}

$\frac{{2 + b}}{b}$ +

\frac{2 + c}{c}

$\frac{{2 + c}}{c}$ = 4, then the value of

\frac{a b + b c + c a}{a b c}

$\frac{{ab + bc + ca}}{{abc}}$ is?", "text": "If

\frac{2 + a}{a}

$\frac{{2 + a}}{a}$ +

\frac{2 + b}{b}

$\frac{{2 + b}}{b}$ +

\frac{2 + c}{c}

$\frac{{2 + c}}{c}$ = 4, then the value of

\frac{a b + b c + c a}{a b c}

$\frac{{ab + bc + ca}}{{abc}}$ is?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{2 + a}{a} + \frac{2 + b}{b} + \frac{2 + c}{c} = 4 \\ \Rightarrow \frac{2 b c + a b c + 2 a c + a b c + 2 a b + a b c}{a b c} = 4 \\ \Rightarrow \frac{2 (b c + a b + c a)}{a b c} + \frac{3 a b c}{a b c} = 4 \\ \Rightarrow \frac{2 (b c + a b + c a)}{a b c} + 3 = 4 \\ \Rightarrow \frac{a b + b c + c a}{a b c} = \frac{1}{2} \end{aligned}

$\eqalign{ & \frac{{2 + a}}{a} + \frac{{2 + b}}{b} + \frac{{2 + c}}{c} = 4 \cr & \Rightarrow \frac{{2bc + abc + 2ac + abc + 2ab + abc}}{{abc}} = 4 \cr & \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + \frac{{3abc}}{{abc}} = 4 \cr & \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + 3 = 4 \cr & \Rightarrow \boxed{\frac{{ab + bc + ca}}{{abc}} = \frac{1}{2}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{2 + a}{a} + \frac{2 + b}{b} + \frac{2 + c}{c} = 4 \\ \Rightarrow \frac{2 b c + a b c + 2 a c + a b c + 2 a b + a b c}{a b c} = 4 \\ \Rightarrow \frac{2 (b c + a b + c a)}{a b c} + \frac{3 a b c}{a b c} = 4 \\ \Rightarrow \frac{2 (b c + a b + c a)}{a b c} + 3 = 4 \\ \Rightarrow \frac{a b + b c + c a}{a b c} = \frac{1}{2} \end{aligned}

$\eqalign{ & \frac{{2 + a}}{a} + \frac{{2 + b}}{b} + \frac{{2 + c}}{c} = 4 \cr & \Rightarrow \frac{{2bc + abc + 2ac + abc + 2ab + abc}}{{abc}} = 4 \cr & \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + \frac{{3abc}}{{abc}} = 4 \cr & \Rightarrow \frac{{2\left( {bc + ab + ca} \right)}}{{abc}} + 3 = 4 \cr & \Rightarrow \boxed{\frac{{ab + bc + ca}}{{abc}} = \frac{1}{2}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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