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If a ,\ b ,\ c ,\ d\ a n d\ p are differ...

If `a ,\ b ,\ c ,\ d\ a n d\ p` are different real numbers such that: `(a^2+b^2+c^2)p^(I2)-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0` , then show that `a ,\ b ,\ c` and `d` are in G.P.

A

A.P.

B

G.P.

C

H.P.

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Here, the given condition `(a^(2) + b^(2) + c^(2)) p^(2) - 2p (ab + bc+ ca) + b^(2) + c^(2) + d^(2) lt 0`
`hArr (p - b)^(2) + (bp - c)^(2) + (cp - d)^(2) lt 0`
`:.` a square can not be negative
`:. ap - b = 0, bc - c = 0, cp - d = 0 hArr p = (b)/(a) = (c)/(b) = (d)/(c) hArr a, b, c, d` are in G.P.
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