Question

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

Answer 1

Answer:

if a,b,c are in continued proportion,

a/b = b/c

from this we get ,

b² = ac .

a² + b² + c²

= a² + ac + c² ( R.H.S )

(a+b+c) (a-b+c)

= a² + ab + ac - ab - b² - bc + ac + bc + c²

= a² + ac + c² ( L.H.S )

as L.H.S = R.H.S , it's proved.