Simple - 4 practice....

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+Î£ab

5 Answers

a SILLY doubt , does

\sum{} ab --------- means ab+bc+cd+da ?

no it means ab+ac+ad+bc+bd+cd

U forgot the word 'positive' ...lol

Open to all 11th graders only.

Okay, 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).....

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