Question

If (a + b + c)(a – b + c) = a² + b² + c² , show that a, b, c are in continued proportion.

Answer 1

(a + b + c)(a – b + c) = a² + b² + c² …[Given] 

∴ a(a – b + c) + b(a – b + c) + c(a – b + c) = a² + b² + c² 

∴ a² – ab + ac + ab – b² + be + ac – be + c² = a² + b² + c² 

∴ a² + 2ac – b² + c² = a² + b² + c²

∴ 2ac – b² = b² 

∴ 2ac = 2b² 

∴ ac = b² 

∴ b² = ac 

∴ a, b, c are in continued proportion.