Let $[t]$ denote the greatest integer $\leq t .$ Then the equation in $x ,[ x ]^{2}+2[ x +2]-7=0$ has

If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are

Let $x, y, z$ be positive integers such that $HCF$ $(x, y, z)=1$ and $x^2+y^2=2 z^2$. Which of the following statements are true?

$I$. $4$ divides $x$ or $4$ divides $y$.

$II$. $3$ divides $x+y$ or $3$ divides $x-y$.

$III$. $5$ divides $z\left(x^2-y^2\right)$.

If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be

If ${\log _2}x + {\log _x}2 = \frac{{10}}{3} = {\log _2}y + {\log _y}2$ and $x \ne y,$ then $x + y = $

$\{ x \in R:|x - 2|\,\, = {x^2}\} = $