[" If "a,b,c" are positive real numbers,then prove that "],[" (i) "b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)>=abc(a+b+c)]

prove that b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)>=abc(a+b+c)

Prove that b^(2)c^(2) + c^(2)a^(2) + a^(2) b^(2) gt abc (a+b+c)

Prove that b^(2)c^(2)+c^(2)a^(2)+a^(2)+b^(2)>abc xx(a+b+c)(a,b,c>0)

If a,b,c are positive unequal real numbers then prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) .

If a,b,c are three distinct positive real numbers prove that (a+b)^(6)+(b+c)^(6)+(c+a)^(6)>192(abc)^(2)

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

If a,b,c are positive real numbers such that a+b+c=1, then prove that (a)/(b+c)+(b)/(c+a)+(c)/(a+b)>=(3)/(2)