Question

If a,b,c are in gp. prove that a2+b2,ab+bc(b2+c2 are in gp

Answer 1

Answer:

Step-by-step explanation:

If a,b,c are in gp. prove that a2+b2, ab+bc , b2+c2 are in gp

a , b , c are in GP

=> b² = ac

a² + b²  , ab + bc , b² + c²  will be in GP

iff

( ab + bc )² = (a² + b²)( b² + c² )

a²b² + b²c² + 2ab²c =  a²b² + a²c² + b⁴ + b²c²

2ab²c = a²c² + b⁴

if we put b² = ac

=> 2ac*ac = a²c² + (ac)²

=> 2a²c² = 2a²c²

LHS = RHS

Hence a² + b²  , ab + bc , b² + c²  will be in GP  if a , b . c are in GP