Let a ,   b ,   c ,   d   and   p be non-zero distinct real numbers such that a 2 + b 2 + c 2 p 2 - 2 ( a b + b c + c d ) p + b 2 + c 2 + d 2 = 0 . Then

Question

Let a , &#160; b , &#160; c , &#160; d &#160; and &#160; p be non-zero distinct real numbers such that a 2 + b 2 + c 2 p 2 - 2 ( a b + b c + c d ) p + b 2 + c 2 + d 2 = 0 . Then

Quantrex Academy · Accepted Answer

Correct answer: C. a , b , c , d &#160; are&#160;in&#160;G.P.

Rearranging the expression, we get ( a p - b ) 2 + ( b p - c ) 2 + ( c p - d ) 2 = 0 &#8658; &#160;&#160; a p - b = 0 , b p - c = 0 , c p - d = 0 &#8658; &#160;&#160; p = b a = c b = d c Which is condition of GP.

Let a ,   b ,   c ,   d   and   p be non-zero distinct real numbers such that a 2 + b 2 + c 2 p 2 - 2 ( a b + b c + c d ) p + b 2 + c 2 + d 2 = 0 . Then

Options

Correct answer

Step-by-step solution

More from Sequences and Series

Let a , &#160; b , &#160; c , &#160; d &#160; and &#160; p be non-zero distinct real numbers such that a 2 + b 2 + c 2 p 2 - 2 ( a b + b c + c d ) p + b 2 + c 2 + d 2 = 0 . Then

Options

Correct answer

Step-by-step solution

More from Sequences and Series

Let a , b , c , d and p be non-zero distinct real numbers such that a 2 + b 2 + c 2 p 2 - 2 ( a b + b c + c d ) p + b 2 + c 2 + d 2 = 0 . Then