If `a x^2+b/xgeqc` for all positive `x` where `a >0` and `b >0,` show that `27 a b^2geq4c^3dot`

If ax^(2)+(b)/(x)>=c for all positive x where a>0 and b>0, show that 27ab^(2)>=4c^(3).

If ax+(b)/(x)>=c for all positive x, where a,b,c>0, then-

If ax+(b)/(x)>=c for all positive xa,b>0, then

If ax+(b)/(x)>=c for all positive x where a,b,>0, then ab =(c^(2))/(4) (c) ab>=(c)/(4) (d) none of these

If (a^(log_b x))^2-5 a^(log_b x)+6=0, where a >0, b >0 & a b!=1, then the value of x can be equal to (a) 2^(log_b a) (b) 3^(log_a b) (c) b^(log_a2) (d) a^(log_b3)

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If all the roots of x^(4)-8x^(3)+24x^(2)+bx+c=0 are positive reals,find |b|

If f(x) = x (1 - log x), " where " x gt 0 , show that (a -b) log c = b (1 - logb) - a(1 - log a), " where " 0 lt a lt c lt b

If x be real and 0