Question

If a, b, c and d are in proportion, prove that: (a – b)/(c – d) = [(3a^2 + 8b^2 )/3c^2 + 8d^2 )]

Answer 1

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

⟹  

b

a

​  

=  

c

b

​  

=  

d

c

​  

=k(say)

⟹c=dk,b=ck=k  

2

d,a=bk=k  

3

d

LHS=(a+d)(b+c)−(a+c)(b+d)=(k  

3

d+d)(k  

2

d+kd)−(k  

3

d+kd)(k  

2

d+d)

                                                                     =d  

2

(k  

5

+k  

2

+k  

4

+k−k  

5

−2k  

3

−k)

                                                                     =k  

2

d  

2

(k−1)  

2

=(k  

2

d−kd)  

2

=(b−c)  

2

=RHS

Hence Proved

Answer 2

Answer:

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