Question

if a,b,c are in A.P, prove that 3a2-4b2+c2=4a(b-c)​

Answer 1

Explanation:

3a²-4b²+c²=4(b-c)a

3a²-3b²+c²-b²=4(b-c)(a)

let.nos.be

b-d , b, b+d

(d is the common difference)

3(a+b) (a-b)+(c+b) (c-b)=4(a) (b-c)

3(2b-d) (-d)+(2b+d) (d)=4(b-d) (-d)

3(d²-2bd)+(2bd+d²)=4(d²-bd)

3d²-6bd+2bd+d²=4d²-4bd= 0

( all cancelled so,0=0)

0=0

hence proved