# the minimum value of ab + bc + cd + de + ef + fg if a + b + c + d + e + f + g=1 if a,b,c,d,e,f,g >0

arvind
39 Points
7 years ago
IT SOULD BE WHAT IS THE MAXIMUM VALUE!
we know (a+b+c+d+e+f+g)^2=a^2+b^2+c^2+d^2+e^2+f^2+g^2+2(sum of numbers taken twice at a time).....................(say)
here we have to find sum of numbers taken twice at a time(X)
a^2+b^2+c^2+d^2+e^2+f^2+g^2 = (a+b+c+d+e+f+g)^2 – 2X

now, a,b,c,.....>0
a^2+b^2+c^2+d^2+e^2+f^2+g^2>0
that implies (a+b+c+d+e+f+g)^2 – 2X>0
2X
2X
X

arvind
39 Points
7 years ago

IT SOULD BE WHAT IS THE MAXIMUM VALUE!
we know (a+b+c+d+e+f+g)^2=a^2+b^2+c^2+d^2+e^2+f^2+g^2+2(sum of numbers taken twice at a time).....................(say)
here we have to find sum of numbers taken twice at a time(X)
a^2+b^2+c^2+d^2+e^2+f^2+g^2 = (a+b+c+d+e+f+g)^2 – 2X

now, a,b,c,.....>0
a^2+b^2+c^2+d^2+e^2+f^2+g^2>0
that implies (a+b+c+d+e+f+g)^2 – 2X>0

final ans X

arvind
39 Points
7 years ago

IT SOULD BE WHAT IS THE MAXIMUM VALUE!
we know (a+b+c+d+e+f+g)^2=a^2+b^2+c^2+d^2+e^2+f^2+g^2+2(sum of numbers taken twice at a time).....................(say)
here we have to find sum of numbers taken twice at a time(X)
a^2+b^2+c^2+d^2+e^2+f^2+g^2 = (a+b+c+d+e+f+g)^2 – 2X
now, a,b,c,.....>0
a^2+b^2+c^2+d^2+e^2+f^2+g^2>0
that implies (a+b+c+d+e+f+g)^2 – 2X>0

final ans X