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.

Sum of the squares of all integral values of a for which the inequality x^(2) + ax + a^(2) + 6a lt 0 is satisfied for all x in ( 1,2) must be equal to

Sum of the squares of all integral values of a for which the inequality x^(2) + ax + a^(2) + 6a lt 0 is satisfied for all x in ( 1,2) must be equal to

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 .

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 .

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 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 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 gt 1 is satisfied for all real values of x

Find the values of x for which the inequality (8x^(2)+16x-51)/((2x-3)(x+4))gt3 holds.