Find the greatest value of xyz for positive values of x, y, z subject to the condition x y+ y z +z x=12 .

Question

Find the greatest value of xyz for positive values of x, y, z subject to the condition x y+ y z +z x=12 . (A) 64 (B) 8 (C) 16 (D) 32

Tardigrade Admin · Accepted Answer

By hit and trial method taking x=y=z=2, we get x y +y z +z x=12 and x y z=8.

Q. Find the greatest value of $x yz$ for positive values of $x, y, z$ subject to the condition $x y + yz + z x = 12$ .