Question : If $a + b + c = 10, a^2 + b^2 + c^2 = 38$, what is the value of $(a - b)^2 + (b - c)^2 + (c - a)^2?$
Option 1: 15
Option 2: 12
Option 3: 14
Option 4: 13
Correct Answer: 14
Solution :
Given: $a + b + c = 10, a^2 + b^2 + c^2 = 38$
So, $(a+b+c)^2=10^2$
⇒ $a^2+b^2+c^2+2(ab+bc+ca)=100$
⇒ $38+2(ab+bc+ca)=100$
⇒ $2(ab+bc+ca)=62$
Now, $(a - b)^2 + (b - c)^2 + (c - a)^2$
= $2(a^2+b^2+c^2)-2(ab+bc+ca)$
= $(2 × 38) - 62$
= $76 -62$
= $14$
Hence, the correct answer is 14.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
