Question

if a b c are in continued proportion prove that a^2+b^2+c^2/(a+b+c)^2=a-b+c/a+b+c​

Answer 1

Step-by-step explanation:

To Prove : (a+b+c)(a−b+c)=a

2

+b

2

+c

2

Proof : a,b,c are in continued proportion.

∴

b

a

=

c

b

=k (let)

b=ck

a=bk=(ck)k =ck

2

L.H.S. =(ck

2

+ck+c)(ck

2

−ck+c)

=c

2

(k

2

+k+1)(k

2

−k+1)

=c

2

[(k

2

+1)

2

−(k)

2

]

=c

2

[k

4

+2k

2

+1−k

2

]

=c

2

[k

4

+k

2

+1]

R.H.S. =c

2

k

4

+c

2

k

2

+c

2

=c

2

[k

4

+k

2

+1]

L.H.S = R.H.S.