UPSC 2016 CDS I Math Paper

(s−a)+(s−b)+(s−c)=s
⇒2s=a+b+c.....(1)
‌‌

(s−a)2+(s−b)2+(s−c)2+s2

a2+b2+c2

=‌‌

4s2−4s2+a2+b2+c2

a2+b2+c2

  [Using(1)]
=1
Trick :
Lest s=5,a=5,b=2,c=3
Then,=

9+4+25

25+4+9

=1
Note:
For solving such type questions, students are advised to select the value of s, a, b and c such that these values must satisfy the given condition.