SSC CHSL 15 Nov 2015 Shift 1 Paper

© examsiri.com

Question : 138 of 199

Marks: +1, -0

If

a ^2 + b^ 2 + c ^2 − ab − bc − ca = 0

then a:b:c is:

1 : 1 : 2
1 : 1 : 1
1 : 2 : 1
2 : 1 : 1

Solution:

Given :

a ^2 + b^ 2 + c ^2 − ab − bc − ca = 0

Multiplying both sides by 2, we get :
⇒

2a ^2 + 2b^ 2 + 2c ^2

− 2ab −2 bc − 2ca = 0

⇒

(a^ 2 − 2ab + b ^2) + (b ^2 − 2bc + c^ 2)

+ (c ^2 − 2ca + a ^2) = 0

⇒

(a − b)^ 2 + (b − c)^2 + (c − a)^ 2 = 0

∵ Sum of three positive sum is 0, then each term is equal to '0'
⇒

(a − b) = (b − c) = (c − a) = 0

⇒ a = b = c
∴

a : b : c = 1 : 1 : 1

© examsiri.com

Go to Question:

Prev Question

Next Question