39a=1 , b=2 , c=4 the result follows
If a,b,c,d are in G.p then show that
(a2+b2+c2) (b2+c2+d2)=(ab+bc+cd)2
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9 Answers
106or u can take a=a, b=ar, c=ar2 and d=ar3 and put the values.... if u want to PROVE it
39well it can be proven normally, also not a difficult one. i am running short of time. sry.
1or use cauchy swartz in equality .. the best .. in which equality holds as
a/b = b/c = c/d
6hey RIDDLE.....i had used ur second method initially but i couldnt get the final answer with it...
1definitely 2nd method is best .. i am sure u will get the answer ...
11Let a = a
let b = ar
let c =ar2
let d = ar3
Now
LHS =
(a2 + a2r2 + a2r4) (a2r6 + a2r2 + a2r4)
a4(1 + r2 +r4)(r2 + r4 + r6)
= a4r2(1 + r2 +r4)(1 + r2 + r4)
= a4r2(1 + + r2 +r4)2
RHS
(a*ar + ar*ar2 + ar2ar3)2
= a4r2( 1 + r2 + r4)2
Hence Proved