it can be proved by using marvelous AM-GM inequality of positive real numbers.Originally Posted byNichelle14

let x=a/(b+c) + b/(a+c) + c/(b+a)

now, b+c>=2(bc)^(1/2)

hence,1/(b+c)<=1/2(bc)^(1/2)

hence,2x<=a/(bc)^(1/2) + b/(ac)^(1/2) + c/(ba)^(1/2)

again applying AM-GM inequality on the right hand side of the equation

2x<=3

x<=3/2