Question

If a,b,c are in AP then show that a2(b+c)+b2(c+a)+c2(a+b) = 2/9(a+b+c)3

explanation is required

if you dont know or can't understand no need to answer​

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+c2k

Answer 2

Answer:

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