Pls help. I tried by using A.M. > G.M relation but it's getting complex. [on hold]

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Let x, y, z, be non negative real numbers satisfying $xyz$ =$2/3$
Find the minimunm value of $ x^2 $+ $6xy $+ $18y^2$ + $12yz $ + $4z^2$




number-theory




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put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco 34 mins ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Hi, if you want to type in MathJax, please use the dollar sign $$ $ to wrap up the math expressions.Example: $$ $ xyz $$$ gives $xyz$.
    – xbh
    21 hours ago











  • $$x^2+6xy+18y^2+12yz+4z^2=(x+3y)^2+(3y+2z)^2gedfrac(x+3y+3y+2z)^22$$
    – lab bhattacharjee
    21 hours ago














up vote
0
down vote

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Let x, y, z, be non negative real numbers satisfying $xyz$ =$2/3$
Find the minimunm value of $ x^2 $+ $6xy $+ $18y^2$ + $12yz $ + $4z^2$




number-theory




share|cite|improve this question













put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco 34 mins ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Hi, if you want to type in MathJax, please use the dollar sign $$ $ to wrap up the math expressions.Example: $$ $ xyz $$$ gives $xyz$.
    – xbh
    21 hours ago











  • $$x^2+6xy+18y^2+12yz+4z^2=(x+3y)^2+(3y+2z)^2gedfrac(x+3y+3y+2z)^22$$
    – lab bhattacharjee
    21 hours ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let x, y, z, be non negative real numbers satisfying $xyz$ =$2/3$
Find the minimunm value of $ x^2 $+ $6xy $+ $18y^2$ + $12yz $ + $4z^2$




number-theory




share|cite|improve this question













Let x, y, z, be non negative real numbers satisfying $xyz$ =$2/3$
Find the minimunm value of $ x^2 $+ $6xy $+ $18y^2$ + $12yz $ + $4z^2$





number-theory





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 21 hours ago
























asked 21 hours ago









Md Masood

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put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco 34 mins ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco 34 mins ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Hi, if you want to type in MathJax, please use the dollar sign $$ $ to wrap up the math expressions.Example: $$ $ xyz $$$ gives $xyz$.
    – xbh
    21 hours ago











  • $$x^2+6xy+18y^2+12yz+4z^2=(x+3y)^2+(3y+2z)^2gedfrac(x+3y+3y+2z)^22$$
    – lab bhattacharjee
    21 hours ago
















  • Hi, if you want to type in MathJax, please use the dollar sign $$ $ to wrap up the math expressions.Example: $$ $ xyz $$$ gives $xyz$.
    – xbh
    21 hours ago











  • $$x^2+6xy+18y^2+12yz+4z^2=(x+3y)^2+(3y+2z)^2gedfrac(x+3y+3y+2z)^22$$
    – lab bhattacharjee
    21 hours ago















Hi, if you want to type in MathJax, please use the dollar sign $$ $ to wrap up the math expressions.Example: $$ $ xyz $$$ gives $xyz$.
– xbh
21 hours ago





Hi, if you want to type in MathJax, please use the dollar sign $$ $ to wrap up the math expressions.Example: $$ $ xyz $$$ gives $xyz$.
– xbh
21 hours ago













$$x^2+6xy+18y^2+12yz+4z^2=(x+3y)^2+(3y+2z)^2gedfrac(x+3y+3y+2z)^22$$
– lab bhattacharjee
21 hours ago




$$x^2+6xy+18y^2+12yz+4z^2=(x+3y)^2+(3y+2z)^2gedfrac(x+3y+3y+2z)^22$$
– lab bhattacharjee
21 hours ago















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