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, c are positive and a + b + c = 1, then find the least value of (1)/(a)+(2)/(b)+(3)/(c)

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 and c are positive real numbers such that a

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))>6abc

Prove that if a,b,c gt 0 then a^2(b+c)+b^2(c+a)+c^2(a+b) geq 6abc

If /_\ ABC is right angled at A, show that: (b^(2) + c^(2))/(b^(2) - c^(2)) .sin (B - C)=1 .

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