If a, b, c, x, y, z are real numbers such that (a + b + c)2 - 3(ab + bc + ca) + 3(x2 + y2 + z2) = 0, then which one of the following is correct?

This question was previously asked in
CDS Elementary Mathematics 3 Sep 2023 Official Paper
View all CDS Papers >
  1. a = b = c, x = y = z ≠ 0
  2. a = b = c = 0, x = y = z = 1
  3. a = b = c, x = y = z = 0
  4. a ≠ b ≠ c, x = y = z = 0

Answer (Detailed Solution Below)

Option 3 : a = b = c, x = y = z = 0
Free
UPSC CDS 01/2025 General Knowledge Full Mock Test
7.9 K Users
120 Questions 100 Marks 120 Mins

Detailed Solution

Download Solution PDF

Given:

(a + b + c)- 3(ab + bc + ca) + 3(x+ y+ z2) = 0

Calculation:

We have

(a + b + c)- 3(ab + bc + ca) + 3(x+ y+ z2) = 0

We solve this question by options 

If we put the value of option 3 then

a = b = c  = k (let) and x = y = z = 0

(k + k + k)2 - 3(k2 + k2 + k2) + 3(0)

⇒ (3k)2 - 3(3k2

⇒ 9k2 - 9k2 = 0

∴ The correct option is 3.

Latest CDS Updates

Last updated on May 29, 2025

-> The UPSC CDS 2 Notification has been released at upsconline.gov.in. for 453 vacancies.

-> Candidates can apply online from 28th May to 17th June 2025.

-> The CDS 2 Exam will be held on 14th September 2025.

-> Attempt UPSC CDS Free Mock Test to boost your score.

-> The selection process includes Written Examination, SSB Interview, Document Verification, and Medical Examination.  

-> Refer to the CDS Previous Year Papers to enhance your preparation. 

Get Free Access Now
Hot Links: teen patti neta online teen patti real money teen patti master 2023 teen patti master apk download teen patti bliss