Question

if a, b, c, d are in continued proportion, then (b - c)² + (c - a)² +(d - b)² = ?​

Answer 1

Answer:

Given A,B,C,D are in continued proportion :-

A/B = B/C = C/D = K ( Say )

C = DK , B = CK = K²D , A = BK = K³D

LHS = ( A+D ) ( B+C ) - ( A+C ) ( B+D ) = ( K³D+D ) ( K²D + KD ) ( K³D + KD ) ( K²D + D )

= K² D² ( K-1² )

Hence , proved

Answer 2

Step-by-step explanation:

A/B=B/C =C/D =k

C=DK,B=CK=K

$}^{2}$

${k}^{2} d$