If a+b+c+d+e=1 , where a, b, c, d & e are positive real numbers then maximum value of a*b + b*c + c*d + d*e =?
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2
1/4
4/25
4/25 is answer
Ur Q seems to wrong because it is olympiad problem and there it is given that a,b,c…are non negative then we find maximum value 1/4
4/25
Tending to 1/4
4/25
0.25 or 1/4
1/5 value 4/25 ans
Ans is 0
0
Put a=b=-1 and c=d=e=1
a=b=1/2
c=d=e=0
ab+bc+cd+de=1/4
i m not sure bcz i included c,d and e as non negative nos.
0
1/4
1/4
(a+b+c….+e)^2 -(a-b+c-d+e)^2 =4(ab+bc+…) so max value occurs only when 2nd sq term is zero then max value is 1 /4 but this can not happen when all terms are positive so a,b, c shold be non negative
1/4 a= 1/2 b = 1/2 rest 0
4/25
Suppose a=1/2 and b=1/2 and c,d,e=0…Satisfy equation….Now a*b=1/4
a=b=e=0 now c=d=1/2 hence it gives max value 1/4
Ans is zero
1/4
a=b=1/2 and c=d= e=0 c,d,are pisitive real no. then ab+bc+cd+de= 1/2*1/2 =1/4