This is my first problem
Algebra
Level
4
X+Y+Z=13, What is the MAXIMUM value of (X-3)(Y-2)(Z+1)???.....
This question is flagged because it is not clearly stated. It likely requires that X, Y, Z are non-negative.
The answer is 27.
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1 solution
X+Y+Z=13 (X-3)+(Y-2)+(Z+1)=9......(1) NOW,Applying A.M-G.M inequality to the above 3 terms , We have, ((X-3)+(Y-2)+(Z-1))^3>=27(X-3)(Y-2)(Z+1) (9)^3>=27(X-3)(Y-2)(Z+1)......(from (1)) 729>=27(X-3)(Y-2)(Z+1). 27.>=(X-3)(Y-2)(Z+1). Hence,the maximum value of (X-3)(Y-2)(Z+1) is 27..