anonymous
  • anonymous
If a b c and d are in G.P, prove that a-b, b-c , c-d are in geometric prgrogression......
Mathematics
katieb
  • katieb
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shubhamsrg
  • shubhamsrg
whats your progress so far ?
anonymous
  • anonymous
i have to solve it back wards......
shubhamsrg
  • shubhamsrg
yep.. you'll have to prove (a-b)(c-d)=(b-c)^2 using ac=b^2

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shubhamsrg
  • shubhamsrg
and ad=c^2 ,also ad=bc
shubhamsrg
  • shubhamsrg
correction: bd=c^2
shubhamsrg
  • shubhamsrg
its upside down,,please re-adjust..
shubhamsrg
  • shubhamsrg
anyways,,i could read it,,and you'll done right till now..i'll write the last step here b^2 + c^2 -2bc = ac+bd-bc-ad
shubhamsrg
  • shubhamsrg
you have to prove LHS = RHS start with any, say LHS
shubhamsrg
  • shubhamsrg
substitute b^2 = ac c^2 = bd
shubhamsrg
  • shubhamsrg
also we know bc=ad so 2bc = bc + ad make these substitutions and there it is..
anonymous
  • anonymous
anonymous
  • anonymous

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