+159 Let a,b,c,d be nonnegative real numbers such that a+b+c+d=1 Find the maximum value of
a2+b2+c2+d2
+6252 The maximum, 1, will occur when one of the variable is 1 and the rest 0
(a+b+c+d−1)=0(a+b+c+d−1)2=0a2+b2+c2+d2−2(a+b+c+d)+2(ab+ac+ad+bc+bd+cd)+1=0a2+b2+c2+d2+2(ab+ac+ad+bc+bd+cd)=1It should be clear that to maximize the sum of the squares we want the second set of terms to be 0This occurs, as noted above when only 1 element is non-zero
