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Question

If a,b,c,d and p are distinct real number such that (a2+b2+c2)p22(ab+bc+cd)p+(b2+c2+d2)0, then a,b,c,d

A
are in A.P
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B
are in G.P
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C
are in H.P
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D
satisfy ab=cd
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E
satisfy none of these
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Solution

The correct option is B are in G.P
(a2+b2+c2)p22(ab+bc+cd)p+(b2+c2+d2)0
(a2p22abp+b2)+(b2p22bcp+c2)+(c2p22cdp+d2)0
(apb)2+(bpc)2+(cpd)20
Sum of square for real numbers can't be negative
Thus ap=b,bp=c,cp=d
ba=cb=dc
a,b,c,dϵ G.P

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