Question : If a, b, c are real and $a^{2}+b^{2}+c^{2}=2(a-b-c)-3, $ then the value of $2a-3b+4c$ is:
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 1
Solution :
Given: $a^{2}+b^{2}+c^{2}=2(a-b-c)-3$.
We can simplify the above equation as follows:
⇒ $a^{2}+b^{2}+c^{2}=2a-2b-2c-3$
⇒ $a^{2}-2a+1+b^{2}+2b+1+c^{2}+2c+1=0$
⇒ $(a-1)^{2}+(b+1)^{2}+(c+1)^{2}=0$
$\therefore a=1, b=-1,c=-1$
Putting the values of $a, b, c$ in $2a-3b+4c$, we get:
$2+3-4=1$
Hence, the correct answer is 1.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
