For all positive values of x, if `ax^(2)+(b)/(x) ge c`(where `a ge 0, b ge0`), prove that, `27ab^(2) ge 4c^(3)`.

If ax+(b)/(x) ge c , for all positive values of x, then show that, 4abgec^(2) , where a,b,c are positive constants.

If ax^2+b/xgec for all positive x where agt0andbgtc show that 27ab^2ge4c^3

The least value of a in RR " for which " 4ax^(2)+(1)/(x)ge1 " for all" xgt0 , is

3(2-x)ge2(1-x)

Exhaustive set of values of x satisfying log_absx(x^2+x+1)ge0 is

Solution set of x satisfying abs(abs(x-2)-1)ge3 is

Solve, (1-sqrt(21-4x-x^(2)))/(x+1) ge 0 .

If a, b, c are positive, prove that (a + b + c) (ab + bc + ca) ge 9abc.

Prove that, 2 sin x+tan x ge3x ,where 0 le x le (pi)/(2) .

The solutions set of the inequation (|x|-4)/(|x|-5)ge0 where x in R and x ne pm5 , are-