Q.
a(1b+1c), b(1c+1a), c(1a+1b) are in AP, then
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a
1a,1b,1c are in AP.
b
a,b,c are in HP
c
1a,1b,1c are in GP
d
a,b,c are in AP.
answer is D.
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Detailed Solution
Given, a(1b+1c), b(1c+1a), c(1a+1b) are in AP.⇒ a(b+c)bc,b(c+a)ca,c(a+b)ab are in AP.⇒ab+acbc+1,bc+abac+1,ca+cbab+1 are in A.P ⇒ab+bc+cabc,ab+bc+caac,ab+bc+caab are in A.P ⇒ 1bc,1ac,1ab are in A.P ⇒a , b ,c are in A.P
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