Question

if a(b+c)=(b^2-c^2)/d and b>c the a is equivalent to
​

Answer 1

Answer:

Step-by-step explanation:

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

2

−b

2

)(c

2

−d

2

)=(k

6

d

2

−k

4

d

2

)(k

2

d

2

−d

2

)=k

4

d

4

(k

2

−1)

2

=(k

4

d

2

−k

2

d

2

)

2

=((k

2

d)

2

−(kd)

2

)

2

=(b

2

−c

2

)

2

=RHS

Hence Proved