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# Engineering

Let a,b,c,d and p be any non zero distinct real numbers such that  (a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)=0 then
Option: 1 a,c,p are in A.P
Option: 2 a,b,c,d are in A.P
Option: 3 a,b,c,d are in G.P
Option: 4 a,c,p are in G.P

Answers (1)
H Himanshu Meshram

If a, b, c, d are in G P

\\\left(a^{2}+a^{2} r^{2}+a^{2} r^{4}\right) p^{2}-2\left(a^{2} r+a^{2} r^{3}+a^{2} r^{5}\right) p+\left(a^{2} r^{2}+a^{2} r^{4}+a^{2} r^{6}\right)=0\\\Rightarrow p^{2}-2 p r+r^{2}=0\\ \Rightarrow(p-r)^{2}=0

Correct Answer: Option C

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