Question

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Answer 1

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Answer 2

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Nishima answered this

Dear student,

a, b, c and d are in continued proportion thenab=bc=cd=k⇒a=bk, b=ck, c=dkTaking left hand side, (a+b)(b+c)−(a+c)(b+d)=ab+ac+b2+bc−(ab+ad+cb+cd)=ab+ac+b2+bc−ab−ad−cb−cd=ac+b2−ad−cd=dk3.dk+(dk2)2−dk3.d−dk.d=d2k4+d2k4−d2k3−d2k=2d2k4−d2k3−d2k=d2(2k4−k3−k)Taking right hand side, (b−c)2=b2+c2−2bc=(dk2)2+(dk)2−2dk2.dk=d2k4+d2k2−2d2k3=d2(k4+k2−2k3)LHS≠RHS

They are not equal