The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is

The roots of the equation $4{x^4} - 24{x^3} + 57{x^2} + 18x - 45 = 0$, If one of them is $3 + i\sqrt 6 $, are

If $3$ distinct real number $a$,$b$,$c$ satisfy $a^2(a + p) = b^2 (b + p) = c^2 (c + p)$ where $p \in R$, then value of $bc + ca + ab$ is

If $a, b, c \in R$ and $1$ is a root of equation $ax^2 + bx + c = 0$, then the curve y $= 4ax^2 + 3bx+ 2c, a \ne 0$ intersect $x-$ axis at

The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:

Let $x$ and $y$ be two $2-$digit numbers such that $y$ is obtained by reversing the digits of $x$. Suppose they also satisfy $x^2-y^2=m^2$ for some positive integer $m$. The value of $x+y+m$ is