11U forgot the word 'positive' ...lol
This is not any biggie.....not my doubt, just wanted to post something after a long time...lol
Find all positive solutions of the system of equations....
a+b+c+d=12
abcd=27+Σab
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5 Answers
11Okay, here's the soln...
Since a+b+c+d=12, with all positive, we get from A.M-G.M that abcd\le 81
Now we apply the same A.M-G.M to abcd-27=\sum{ab}
If \sqrt{abcd}=x then we again have abcd\ge 81 \Rightarrow abcd=81
Since inequality in A.M-G.M holds when a=b=c=d, we have the unique soln as \left(3,3,3,3 \right).....