If a² + b² + c² - ab - bc - ca = 0, then a ∶ b ∶ c is :

Question

Question

This question was previously asked in

Haryana CET Previous Year Paper (Held On: 6 Nov 2022 Shift 2)

Answer 1

Given :

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

Solution :

Here we have 3 variables and only one equation .

Note: To solve these type of question we assume the value of any 2 variables.

Let assume that b = 1 and c = 1

⇒ a²+ 1 + 1 - a - 1 - a = 0

⇒ a² + 1 - 2a = 0

⇒ ( a - 1 )² = 0 [ ∵ ( A + B )² = A² + B² + 2AB ]

Now a = 1

Now we have a = 1, b = 1 and c = 1

So a : b : c = 1 : 1 : 1

Hence the correct answer is "1 : 1 : 1".