if four positive no. a b c d are in gp such that a*b*c*d=5184, then what is the maximum value of b

• if they are in gp then terms will be like a,ar^2,ar^3,...
  so here a=a
  b=ar
  c=ar^2
  d=ar^3
  so,abcd=a(ar)(ar^2)(ar^3)=5184
  (a^4)*(r^6)=(3^4)*(2^6)=a=4,r=6
  here b=ar=3*2=6
• 6 years agoHelpfull: Yes(1) No(2)
• 9
  b^2=ac;
  c^2=bd;
  (bc)^2=5184
  bc=72
  b==9 and c==8
  or b=8 c=9
  max b=9
• 5 years agoHelpfull: Yes(1) No(2)
• max b=12
  r=2
  a,b,c,d=24, 12, 6, 3 are also in gp
  so b=12 (max value possible)
• 5 years agoHelpfull: Yes(1) No(0)
• max b=12
  r=1/2
  a=24
  b=12
  c=6
  d=3
  a,b,c,d=24, 12, 6, 3 are also in gp
  so b=12 (max value possible)
• 5 years agoHelpfull: Yes(1) No(0)
• a*b*c*d=5184=4^3*(9^2)
  b/a=c/b=d/c (a,b,c and d are in GP)
  b^2=a*c
  b^3*d=4^3* 81
  b=4
• 6 years agoHelpfull: Yes(0) No(1)
• A,B,C,D are in GP
  So,
  A=a
  B=ar
  C=ar^2
  D=ar^3
  A*B*C*D=(r^6 )*(a^4)
  5184=(2^6)*(3^4)
  Comparing we get,
  r=2
  a=3
  B=6
• 5 years agoHelpfull: Yes(0) No(0)
• they are in gp then terms will be like a,ar^2,ar^3,...
  so here a=a
  b=ar
  c=ar^2
  d=ar^3
  so,abcd=a(ar)(ar^2)(ar^3)=5184
  (a^4)*(r^6)=(3^4)*(2^6)=a=4,r=6
  here b=ar=3*2=6
• 9 Months agoHelpfull: Yes(0) No(0)