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

1 thought on “if a, b, c are in continued proportion, show that a^2+b^2/b(a+c)=b(a+c)/b^2+c^2​”

1. Answer:

   here is your answer mate

   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.

   hope it’s helpful to you!

   Reply