Question

If a² + b² + c² = ab + bc + ac then the value of `(a + c)/b` is

Options

• 0

• 2

• 1

• – 1

Answer 1

2

Explanation:

a² + b² + c² = ab + bc + ca

⇒ a² + b² + c² – ab – bc – ca = 0

On multiplying by 2,

2a² + 2b² + 2c² – 2ab – 2bc – 2ca = 0

⇒ a² + b² – 2ab + b² + c² – 2abc + c² + a² + 2ac = 0

⇒ (a – b)² + (b – c)² + (c – a)² = 0

⇒ a – b = 0

⇒ a = b

b – c = 0 ⇒ b = c

c – a = 0 ⇒ c = a

∴ `(a + c)/b = (2a)/a` = 2