[" The least value of "alpha in R," for "],[" which "^(4 alpha x^(2)+(1)/(x)>=1)," for all "x>0,],[" is "]

The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for all xgt0, is

The least value of alpha in R for which 4ax^2+(1)/(x)ge1 , for all xgt 0 , is

The least value of a in R for which 4ax^(2)+(1)/(x)>=1, for all x>0, is

Let f : R - {(alpha )/(6) } to R be defined by f (x) = ( 3x + 3)/(6x - alpha). Then the value of alpha for which (fof) (x) = x , for all x in R -{(alpha)/(6)}, is :

The set of all values of alpha for which x^(2)-9+|x+sin alpha|<0 has a solution is

The values of alpha in R for which the quadratic equation 3x^(2)+2(alpha^(2)+1)x+(alpha^(2)-3 alpha+2)=0 possesses real roots of opposite sign are

Find all the values of alpha for which the equation sin ^(4) x+ cos^(4)x+ sin 2x +alpha=0 is valid.

Find all the values of alpha for which : sin^4 x + cos^4 x + sin 2x +alpha =0 is valid.