Question

If xyz = cost. find the minimum value of xy+yz+zx​

Answer 1

Since (x+y+z)2=x2+y2+z2+2(xy+xz+yz)

=1+2(xy+xz+yz)

(x+y+z)2≥0

So that 1+2(xy+xz+yz)≥0

(xy+xz+yz)≥−12

So the minimum value is −12.