Hi Underdog,
What i understand is - If (a + b + c) { hereafter, will be referred as A } is max, then ( a + b + c)^2 is also maximum..
Here, since the sum of suares of a. b & c are given, we need to see the relation b/w the given value n the required one.
So, A^ 2 = a ^2 + b^2 + c^2 + 2(ab + bc + ca)
Let the 1st 3 terms in RHS be B.
Now, B is given to be 48.
for LHS ( A^2) to be max, only thing we can maximise would be the second term of RHS since B is constant ( = 48).
Now we have B = 48, so we'll get the max product if we have all its terms equal... rest follows..
Thanks
SP |