If a, b, c are real and distinct, then show that `a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)>6a b c`

Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc .

Show that a^(2)(1+b^(2))+b^(2)(1+c^(2))+c^(2)(1+a^(2))gt abc

Show that a^(2)(1+b^(2))+b^(2)(1+c^(2))+c^(2)(1+a^(2))gt abc

If a, b, c are distinct real numbers, show that the points (a, a^2), (b, b^2) and (c, c^2) are not collinear.

If a,b,c are three distinct positive real number such that a^2+b^2+c^2=1 , then ab+bc+ca=1 is

If a,b, and c are positive and a+b+c=6 show that (a+1/b)^(2)+(b+1/c)^(2)+(c+1/a)^(2)>=75/4

If a, b, c are distinct real numbers such that a, b, c are in A.P. and a^2, b^2, c^2 are in H. P , then

If a,b,c are distinct real numbers such that a, b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P, then

If a, b and c are positive real numbers such that a

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