If `a ,b ,a n dc` are positive and `a+b+c=6,` show that `(a+1//b)^2+(b+1//c)^2+(c+1//a)^2geq75//4.`

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 ,a n dc are in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

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

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

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

If a, b, c are positive real numbers then show that (i) (a + b + c) ((1)/(a) + (1)/(b) +(1)/(c)) ge 9 (ii) (b+c)/(a) +(c +a)/(b) + (a+b)/(c) ge 6

If a, b, c are positive real numbers then show that (i) (a + b + c) ((1)/(a) + (1)/(b) +(1)/(c)) ge 9 (ii) (b+c)/(a) +(c +a)/(b) + (a+b)/(c) ge 6

If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove that (1-a)(1-b)(1-c)> 8.

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove that ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.