Exact set of values of a for which `x^3(x + 1) = 2(x + a) (x + 2a)` is having four real solutions is

The set of values of a for which f(x)=x^(3)-ax^(2)+48x+1 is increasing for all real values of x is

The set of values for which x^(3)+1 ge x^(2)+x is

The largest set of real values of x for which f(x)=sqrt((x + 2)(5-x))-1/sqrt(x^2-4) - is a real function is

The largest set of real values of x for which ln(1+x)<=x is

The set of values of c for which x^3 -6x^2 + 9x -c is of the form (x-a)^2(x - b) (a, b is real) is given by

Let f(x)=x^(2)+kx;k is a real number.The set of values of k for which the equation f(x)=0 and f(f(x))=0 have same real solution set.

The largest set of real values of x for which f(x)=sqrt((x+2)(5-x))-(1)/(sqrt(x^(2)-4))- is a real function is

The set of real values of x for which log_ 0.2((x+2)/x) ≤1 is

The set of real values of x for which (10x^2 +17x-34)/(x^2 + 2x - 3) < 8, is

Find the values of a for which the equation ||x-2|+a|=4 can have four distinct real solutions.