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Question

If a,b,c are in A.P. and a2,b2,c2 are in G.P. such that a<b<c and a+b+c=34, then the value of a is :

A
14
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B
14122
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C
14+122
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D
14142
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Solution

The correct option is B 14122
a,b,c are in A.P.
2b=a+c ...(1)

a2,b2,c2 are in G.P.
(b2)2=a2c2 ...(2)
a+b+c=34 ...(3)

From equation (1) and (3)
2b+b=34 b=14
From equation (2)
a2c2=(116)2
ac=±116
a(12a)=±116 (From equation (1), a+c=12)

Case 1:
a(12a)=+116
2a2a+18=0
a=1±114=14

Case 2:
a(12a)=116
2a2a18=0
a=1±1+14=1±24
a=14+122, 14122
a=14122
(a<b<c)

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