Let a,b,c be in G.P. If x,y are arithmetic means between a,b and b,c respectively, then which of the following is/are correct?
A
1x+1y=1b
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B
1x+1y=2b
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C
ax+cy=1
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D
ax+cy=2
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Solution
The correct options are B1x+1y=2b Dax+cy=2 a,b,c are in G.P. ⇒b2=ac Now, x=a+b2,y=b+c2 1x+1y=2a+b+2b+c=2[b+c+a+b(a+b)(b+c)]=2[2b+a+cab+ac+b2+bc] =2[2b+a+c2b2+ab+bc](∵ac=b2) =2b(2b+a+c)(2b+a+c)=2b