The greatest value of xyz for +ve values of x,y,z ; where yz+zx+xy=12 is
4
6
8
10
The explanation for the correct answer.
Find the greatest value.
Given: yz+zx+xy=12
Using the relation AM ≥GM, AM is Arithmetic Mean and GM is Geometric Mean.
xy+yx+zx3≥x2y2z213⇒4≥xyz23⇒432≥xyz⇒8≥xyz
Hence option (c) is the correct answer.