lf `abcd=1` where a,b,c,d are positive reals then the minimum value of `a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd` is

If a, b and c are all positive real, then prove that minimum value of determinant |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ac,bc,c^2+1):}| = 1+a^2+b^2+c^2

Find the minimum value of abs[[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]]

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

If a: b= 5:7 and c:d=2a:3b, then ac: bd is :

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 such that a,b,c are in A.P. and b,c,d are in H.P., then : (A) ab=cd (B) ac=bd (C) ad=bc (D)none of these

Let a,b,c , d ar positive real number such that a/b ne c/d, then the roots of the equation: (a^(2) +b^(2)) x ^(2) +2x (ac+ bd) + (c^(2) +d^(2))=0 are :

Let a,b,c , d ar positive real number such that a/b ne c/d, then the roots of the equation: (a^(2) +b^(2)) x ^(2) +2x (ac+ bd) + (c^(2) +d^(2))=0 are :