If `a ,b ,c` are positive, then prove that `a//(b+c)+b//(c+a)+c//(a+b)geq3//2.`

If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2 .

If a^(2),b^(2) and c^(2) are in AP then prove that (a)/(b+c),(b)/(c+a) and (c)/(a+b) are also in A.P.

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)

If a,b,c are positive reral numbers such that (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then prove that

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

If s=a+b+c+d where a, b, c, d are positive unequal numbers then prove that (s-a)(s-b)(s-c)(s-d) geq 81abcd .

If a,b,c, are in AP, prove that a^(3) + 4b^(3)+c^(3)= 3b (a^(2)+c^(2))

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

If A=2B, then prove that either c=b or a^(2)=b(c+b)

If (b^2+c^2-a^2)/(2b c),(c^2+a^2-b^2)/(2c a),(a^2+b^2-c^2)/(2a b) are in A.P. and a+b+c=0 then prove that a(b+c-a),b(c+a-b),c(a+b-c) are in A.P.