Question

if a b c d are in continued proportion . prove that ad(c^2+d^2)=c^3(b+d)

Answer 1

Answer:

a,b,c,d are in continued proportion

⇒

b

a

=

c

b

=

d

c

=k

⇒a=bk,b=ck,c=dk,

To prove a

2

+b

2

+c

2

)(b

2

+c

2

+d

2

)=(ab+bc+cd+)

2

substituting a,b,c

⇒((bk)

2

+(ck)

2

+(dk)

2

)(b

2

+c

2

+d

2

)=(b

2

k+c

2

k+d

2

k)

2

⇒k

2

(b

2

+c

2

+d

2

)(b

2

+c

2

+d

2

)=k

2

(b

2

+c

2

+d

2

)

2

⇒(b

2

+c

2

+d

2

)

2

=(b

2

+c

2

+d

2

)

2

Hence proved.