Question

If a,b,c,d are in continued proportion, prove that:
(a+b)(b+c)-(a+c)(b+d)=(b-c)²​

Answer 1

n Figure line AB || line CD and line PQ is the

transversal. Ray PT and ray QT are bisectors of

BPQ and PQD respective

Step-by-step explanation:

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Answer 2

Answer:

here is your Solution

 Given a,b,c,d are in continued proportion

⟹ba=cb=dc=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)

                                                                      =d2(k5+k2+k4+k−k5−2k3−k)

                                                                      =k2d2(k−1)2=(k2d−kd)2=(b−c)2=RHS

Hence Proved

Step-by-step explanation:

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