Grade 11Algebra
Let a,b,c € R. a+b+c=4, then find the maximum value of (ab+bc+ac).
1 Answer
Arun
square a+b+c to get a^2 + b^2 + c^2 + 2(ab+bc+ca) = 4.
Note that a^2 + b^2 + c^2 >= ab + bc + ca by AM-GM.
thus ab + bc + ca
Hence
ab + bc + ca = 16/9 + 16/9 + 16/9
= 48/9
= 16/3
Regards
Arun (askIITians forum expert)
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