If a, b, c and d are positive real numbers such that a+b+c+d= 1 then prove that `ab + bc + cd + da le 1/4`.

If a, b, c, d are positive numbers in HP then prove that ad gt bc .

If a,b,c,d are four positive real numbers such that abcd=1 then least value of (a+4)(b+4)(c+4)(d+4) is

If a,b,c,d,e and f are non negative real numbers such that a+b+c+d+e+f=1, then the maximum value of ab+bc+cd+de+ef is

If a,b,c and d are four positive real numbers such that abcd =1, what is the minimum value of (1+a)(1+b)(1+c)(1+d)

If a,b, and c are distinct positive real numbers and a^(2)+b^(2)+c^(2)=1, then ab+bc+ca is

If a,b,c are positive real numbers such that a+b+c=1 , then find the minimum value of (1)/(ab)+(1)/(bc)+(1)/(ac) .

If a, b, c, d and p are distinct real numbers such that (a^(2) + b^(2) + c^(2)) p^(2) - 2(ab + bc + cd) p + (b^(2) + c^(2) + d^(2)) le 0 , then a, b, c, d are in