If a+bxa−bx=b+cxb−cx=c+dxc−dx(x≠0), then a,b,c,d are in
A
A.P.
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B
G.P.
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C
H.P.
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D
none of these
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Solution
The correct option is B G.P. From 1st two, by cross-multiplication, we get (a+bx)(b−cx)=(b+cx)(a−bx) ⇒2x(b2−ac)=0⇒b2−a=0asx≠0 Similarly from 2nd and 3rd, we get (c+dx)(b−cx)=(b+cx)(c−dx) ⇒2x(c2−bd)=0 ⇒c2=bd ∴ab=bc=cd⇒a,b,c,d are in G.P.