Question

If a, b, care in continued proportion prove that
(a square+ab square+b square)÷(a square+ac square+c square)=(b square)÷(b square-bc square+c square)​

Answer 1

Step-by-step explanation:

To Prove : (a+b+c)(a−b+c)=a2+b2+c2

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

∴          ba=cb=k (let)

                                 b=ck

                                 a=bk=(ck)k =ck2

L.H.S. =(ck2+ck+c)(ck2−ck+c)

           =c2(k2+k+1)(k2−k+1)

           =c2[(k2+1)2−(k)2]

           =c2[k4+2k2+1−k2]

           =c2[k4+k2+1]

R.H.S. =c2k4+c

So, LHS=RHS.