Find all values of the parameter a for which the inequality `a.9^x +4(a-1)3^x+a gt 1` is satisfied for all real values of x

Find all values of the parameter a for which the inequality a.9^(x)+4(a-1)3^(x)+a>1 is satisfied for all real values of x

Find all values of a for which the inequation 4^(x^(2))+2(a+1)2^(x^(2))+4a^(2)-3gt0 is satisfied for any x .

If t is a real number satisfying the equation 2t^(3)-9t^(2)+30-a=0, then find the values of the parameter a for which the equation x+(1)/(x)=t gives six real and distinct values of x .

the smallest integral value of p for which the inequality (p-3)x^(2)-2px+3(p-2)>0 is satisfied for all real values of x, is

The number of positive integral values of the parameter a such that the inequality a- (x^(2))/(5)>sqrt(25-x^(2)) is not satisfied by all values of x in [-5,5] ,is

If the equation x^(2)+9y^(2)-4x+3=0 is satisfied for all real values of x and y, then

Find all values of a for which the inequality (a+4)x^(2)-2ax+2a-6<0 is satisfied for all x in R.

Find all values of k for which the inequality, 2x^(2)-4k^(2)x-k^(2)+1gt0 is valid for all real x which do not exceed unity in the absolute value.

The number of integral values of K the inequality |(x^(2)+kx+1)/(x^(2)+x+1)|<3 is satisfied for all real values of x is...]|

If the inequality (mx^(2)+3x+4)/(x^(2)+2x+2)<5 is satisfied for all x in R, then find the value of m.