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Q. . If x 1 ,x 2 , ………….x n are n non-zero real numbers such that (x 1 2 +x 2 2 + …..+x (n-1) 2 )(x 2 2 +x 3 2 + …..+x n 2 ) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn) 2 , then x 1 ,x 2……………………. x n are in (a) A.P. (b) G.P. (c) H.P. (d) none of these

Q. .    If x1,x2, ………….xn are n non-zero real numbers such that


  (x12+x22+ …..+x(n-1)2)(x22+x32+ …..+xn2) ≤ (x1,x2+ x2,x3+…….+ xn-1,xn)2,


 then x1,x2……………………. xare in


(a)   A.P.


(b)    G.P.


(c)    H.P.


(d)    none of these

Grade:Upto college level

1 Answers

aman bansal
askIITians Faculty 33 Points
11 years ago

dear raghu,

the above question can be solved by expanding the terms and then converting it into a perfect square

for simplicity  we can take n=3 and then conclude that it forms GP

hence answer is (B)


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AMAN BANSAL

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