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Question
if `(a+ bx)/(a - bx) = (b +cx)/(b - cx) = (c + dx)/(c- dx) (x != 0)` then show that a, b, c and d are in G.P.
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Solution
We know that if `"a"/"b" = "c"/"d"` then `("a" + "b")/("a" - "b") = ("c" + " d")/("c" - "d")`
According to this rule, if `("a" + "bx")/("a" - "bx") = ("b" + "cx")/("b" - "cx") = ("c" + "cx")/("c" - "cx")`
So, `(("a" + "bx") + ("a" - "bx"))/(("a" + "bx") - ("a" - "bx")) = ((" b" + "cx") + ("b" - "cx"))/(("b" + "cx") - ("b" - "cx"))`
= `(("c" + "dx") + ("c" - "dx"))/(("c" + "dx") - ("c" - "dx"))`
`(2"a")/(2"bx") = (2"b")/(2"cx") = (2"c")/(2"dx")`
or `"a"/"b" = "b"/"c" = "c"/"d"`
Hence a, b, c, d are in geometric progression.
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