1yup correct!
now post the soln [1]
let a,b,c and d be four distinct integers.....the find the smallest possible value of
4(a^{2}+b^{2}+c^{2}+d^{2})-(a+b+c+d)^{2}
-
UP 0 DOWN 0 0 4
4 Answers
13Expand (a+b+c+d)2.....
The situation now reduces to - (Min. value of)-
3(a2+b2+c2+d2) - 2(ab+ac+ad+bc+bd+cd)
V can easily show tht -
3(a2+b2+c2+d2) ≥ 2(ab+ac+ad+bc+bd+cd).
So, v figure out tht the expression wud hold the least possible value when, a,b,c,d hold their least possible +ve values i.e. 1,2,3,4 (Four distinct integers, the case can also be like -1,-2,-3,-4,etc. but end result same.)
So, smallest possible value = 20.