Question

a2 + b2 + 2c2 = ab + 2bc+ 2ca. Prove that a = b =c

Answer 1

I think your answer needs some corrctions.

If 2a² + 2b² + 2c² = 2ab + 2bc + 2ca, prove that a = b = c

Answer is given below :

Now,

2a² + 2b² + 2c² = 2ab + 2bc + 2ca

⇒ a² - 2ab + b² + b² - 2bc + c² + c² - 2ca + a² = 0

⇒ (a - b)² + (b - c)² + (c - a)² = 0

We know that, if the sum of square terms be zero, then each term equals to zero.

So, a - b = 0 ⇒ a = b

b - c = 0 ⇒ b = c

c - a = 0 ⇒ c = a

Thus, combining, we get a = b = c. [Proved]

I hope that it helps you.

Answer 2

here is your answer

hope it helps