((a^2+a+1)+(b^2+b+1)+(c^2+c+1)+(d^2+d+1)+(e^2+e+1))/abcde,where a,b,c,d,e are positive integers then find the minimum value of the above expression.

• lets consider (a^2+a+1)/a=y
  so, dy/da= a^2-1/a^2
  so, dy/da=0
  a^2-1/a^2=0
  a=1 or -1
  now d2y/da2 = 2/a^3
  so for min, d2y/da2 should be max which is at a=1
  so similarly a=b=c=d=e=1
  so the above expression yields 15 as the minimum value
• 10 years agoHelpfull: Yes(1) No(0)